메뉴 건너뛰기




Volumn 5, Issue 1, 2001, Pages 1-74

Planarizing graphs - A survey and annotated bibliography

Author keywords

[No Author keywords available]

Indexed keywords

UNDIRECTED GRAPHS;

EID: 0013157887     PISSN: 15261719     EISSN: None     Source Type: Journal    
DOI: 10.7155/jgaa.00032     Document Type: Review
Times cited : (88)

References (322)
  • 1
    • 84947903127 scopus 로고    scopus 로고
    • Quasi-Planar Graphs Have a Linear Number of Edges
    • [AAP+96] Franz J. Brandenburg, editor, Springer-Verlag, Lecture Notes in Computer Science
    • [AAP+96] Pankaj K. Agarwal, Boris Aronov, János Pach, Richard Pollack, and Micha Sharir. Quasi-Planar Graphs Have a Linear Number of Edges. In Franz J. Brandenburg, editor, Graph Drawing. Proceedings of the DIMACS International Workshop, GD'95, pages 1-7. Springer-Verlag, Lecture Notes in Computer Science, vol. 1027, 1996.
    • (1996) Graph Drawing. Proceedings of the DIMACS International Workshop, GD'95 , vol.1027 , pp. 1-7
    • Agarwal, P.K.1    Aronov, B.2    Pach, J.3    Pollack, R.4    Sharir, M.5
  • 2
    • 84987467105 scopus 로고
    • Little. An Algebraic Characterization of Planar Graphs
    • [ABL95]
    • [ABL95] Dan Archdeacon, C. Paul Bonnington, and Charles H.C. Little. An Algebraic Characterization of Planar Graphs. J. of Graph Theory, 19:237-250, 1995.
    • (1995) J. of Graph Theory , vol.19 , pp. 237-250
    • Archdeacon, D.1    Bonnington, C.P.2    Charles, H.C.3
  • 4
    • 0004542029 scopus 로고
    • The thickness of an arbitrary complete graph
    • [AG76] In Russian
    • [AG76] V.B. Alekseev and V.S. Goncakov. The thickness of an arbitrary complete graph. Mat. Sbornik, 101(143):212-230, 1976. In Russian.
    • (1976) Mat. Sbornik , vol.101 , Issue.143 , pp. 212-230
    • Alekseev, V.B.1    Goncakov, V.S.2
  • 5
    • 0026082425 scopus 로고
    • Multilayer Grid Embeddings for VLSI
    • [AKS91]
    • [AKS91] Alok Aggarwal, Maria Klawe, and Peter Shor. Multilayer Grid Embeddings for VLSI. Algorithmica, 6:129-151, 1991.
    • (1991) Algorithmica , vol.6 , pp. 129-151
    • Aggarwal, A.1    Klawe, M.2    Shor, P.3
  • 7
    • 4043084350 scopus 로고
    • On the toroidal thickness of graphs
    • [And82a]
    • [And82a] Ian Anderson. On the toroidal thickness of graphs. J. of Graph Theory, 6:177-184, 1982.
    • (1982) J. of Graph Theory , vol.6 , pp. 177-184
    • Anderson, I.1
  • 8
    • 4043091527 scopus 로고
    • The Toroidal Thickness of the Symmetric Quadripartite Graph
    • [And82b]
    • [And82b] Ian Anderson. The Toroidal Thickness of the Symmetric Quadripartite Graph. J. of Combinatorial Theory, Series B, 33:57-59, 1982.
    • (1982) J. of Combinatorial Theory, Series B , vol.33 , pp. 57-59
    • Anderson, I.1
  • 10
    • 85039504265 scopus 로고
    • The edge-outercoarseness of complete graphs
    • [AP93]
    • [AP93] D.G. Akka and S.V. Panshetty. The edge-outercoarseness of complete graphs. Bull. Cal. Math. Soc., 85:505-512, 1993.
    • (1993) Bull. Cal. Math. Soc. , vol.85 , pp. 505-512
    • Akka, D.G.1    Panshetty, S.V.2
  • 11
    • 84986517529 scopus 로고
    • Face Colorings of Embedded Graphs
    • [Arc84]
    • [Arc84] Dan Archdeacon. Face Colorings of Embedded Graphs. J. of Graph Theory, 8:387-398, 1984.
    • (1984) J. of Graph Theory , vol.8 , pp. 387-398
    • Archdeacon, D.1
  • 13
    • 38249034532 scopus 로고
    • On the genus and thickness of graphs
    • [Asa87]
    • [Asa87] Kouhei Asano. On the genus and thickness of graphs. J. of Combinatorial Theory, Series B, 43:287-292, 1987.
    • (1987) J. of Combinatorial Theory, Series B , vol.43 , pp. 287-292
    • Asano, K.1
  • 14
    • 4043118509 scopus 로고
    • On the thickness of graphs with genus 2
    • [Asa94]
    • [Asa94] Kouhei Asano. On the thickness of graphs with genus 2. Ars Combinatoria, 38:87-95, 1994.
    • (1994) Ars Combinatoria , vol.38 , pp. 87-95
    • Asano, K.1
  • 15
    • 0038580932 scopus 로고
    • Generating the triangulations of the projective plane
    • [Bar82]
    • [Bar82] D.W. Barnette. Generating the triangulations of the projective plane. J. of Combinatorial Theory, Series B, 33:222-230, 1982.
    • (1982) J. of Combinatorial Theory, Series B , vol.33 , pp. 222-230
    • Barnette, D.W.1
  • 17
    • 0039110965 scopus 로고
    • Generating closed 2-cell embeddings in the torus and the projective plane
    • [Bar87]
    • [Bar87] D.W. Barnette. Generating closed 2-cell embeddings in the torus and the projective plane. Discrete Comput. Geom., 2:233-247, 1987.
    • (1987) Discrete Comput. Geom. , vol.2 , pp. 233-247
    • Barnette, D.W.1
  • 18
    • 38249017246 scopus 로고
    • Generating the 4-connected and strongly 4-connected triangulations on the torus and projective plane
    • [Bar90]
    • [Bar90] D.W. Barnette. Generating the 4-connected and strongly 4-connected triangulations on the torus and projective plane. Discrete Mathematics, 85(1):1-16, 1990.
    • (1990) Discrete Mathematics , vol.85 , Issue.1 , pp. 1-16
    • Barnette, D.W.1
  • 20
    • 4043172159 scopus 로고
    • Note on t-minimal complete bipartite graphs
    • [BB68]
    • [BB68] I.Z. Bouwer and I. Broere. Note on t-minimal complete bipartite graphs. Canad. Math. Bull., 11:729-732, 1968.
    • (1968) Canad. Math. Bull. , vol.11 , pp. 729-732
    • Bouwer, I.Z.1    Broere, I.2
  • 21
    • 84987492877 scopus 로고
    • New Results on Rectilinear Crossing Numbers and Plane Embeddings
    • [BD92]
    • [BD92] Daniel Bienstock and Nathaniel Dean. New Results on Rectilinear Crossing Numbers and Plane Embeddings. J. of Graph Theory, 16:389-398, 1992.
    • (1992) J. of Graph Theory , vol.16 , pp. 389-398
    • Bienstock, D.1    Dean, N.2
  • 22
    • 84987564484 scopus 로고
    • Bounds for rectilinear crossing numbers
    • [BD93]
    • [BD93] Daniel Bienstock and Nathaniel Dean. Bounds for rectilinear crossing numbers. J. of Graph Theory, 17:333-348, 1993.
    • (1993) J. of Graph Theory , vol.17 , pp. 333-348
    • Bienstock, D.1    Dean, N.2
  • 23
    • 51249173713 scopus 로고
    • All Orientable 2-Manifolds Have Finitely Many Minimal Triangulations
    • [BE88]
    • [BE88] D.W. Barnette and A.L. Edelson. All Orientable 2-Manifolds Have Finitely Many Minimal Triangulations. Israel J. of Mathematics, 62:90-98, 1988.
    • (1988) Israel J. of Mathematics , vol.62 , pp. 90-98
    • Barnette, D.W.1    Edelson, A.L.2
  • 24
    • 51249173602 scopus 로고
    • All 2-Manifolds Have Finitely Many Minimal Triangulations
    • [BE89]
    • [BE89] D.W. Barnette and A.L. Edelson. All 2-Manifolds Have Finitely Many Minimal Triangulations. Israel J. of Mathematics, 67:123-128, 1989.
    • (1989) Israel J. of Mathematics , vol.67 , pp. 123-128
    • Barnette, D.W.1    Edelson, A.L.2
  • 25
    • 4043176433 scopus 로고
    • Complete Bipartite Graphs: Decomposition into Planar Subgraphs
    • [Bei67] Frank Harary, editor, Holt, Rinehart and Winston
    • [Bei67] Lowell W. Beineke. Complete Bipartite Graphs: Decomposition into Planar Subgraphs. In Frank Harary, editor, A Seminar on Graph Theory. Holt, Rinehart and Winston, 1967.
    • (1967) A Seminar on Graph Theory
    • Beineke, L.W.1
  • 26
    • 0041642539 scopus 로고
    • Minimal decompositions of complete graphs
    • [Bei69]
    • [Bei69] Lowell W. Beineke. Minimal decompositions of complete graphs. Can. J. Math., 21:992-1000, 1969.
    • (1969) Can. J. Math. , vol.21 , pp. 992-1000
    • Beineke, L.W.1
  • 28
    • 0004249508 scopus 로고
    • [Ber73] Claude Berge. North-Holland
    • [Ber73] Claude Berge. Graphs and Hypergraphs. North-Holland, 1973.
    • (1973) Graphs and Hypergraphs
  • 29
    • 0003878763 scopus 로고
    • [Ber89] North-Holland
    • [Ber89] Claude Berge. Hypergraphs. North-Holland, 1989.
    • (1989) Hypergraphs
    • Berge, C.1
  • 30
    • 4043159350 scopus 로고
    • The coarseness of the complete bipartite graph
    • [BG69]
    • [BG69] Lowell W. Beineke and Richard K. Guy. The coarseness of the complete bipartite graph. Can. J. Math., 21:1086-1096, 1969.
    • (1969) Can. J. Math. , vol.21 , pp. 1086-1096
    • Beineke, L.W.1    Guy, R.K.2
  • 31
    • 0040794967 scopus 로고
    • The thickness of the complete graph
    • [BH65]
    • [BH65] Lowell W. Beineke and Frank Harary. The thickness of the complete graph. Can. J. Math., 17:850-859, 1965.
    • (1965) Can. J. Math. , vol.17 , pp. 850-859
    • Beineke, L.W.1    Harary, F.2
  • 32
  • 33
    • 0004513506 scopus 로고
    • On the thickness of the complete bipartite graph
    • [BHM64]
    • [BHM64] Lowell W. Beineke, Frank Harary, and John W. Moon. On the thickness of the complete bipartite graph. Proc. Camb. Phil. Soc., 60:1-5, 1964.
    • (1964) Proc. Camb. Phil. Soc. , vol.60 , pp. 1-5
    • Beineke, L.W.1    Harary, F.2    Moon, J.W.3
  • 34
    • 51249175187 scopus 로고
    • Some Provably Hard Crossing Number Problems
    • [Bie91]
    • [Bie91] Daniel Bienstock. Some Provably Hard Crossing Number Problems. Discrete Comput. Geom., 6:443-459, 1991.
    • (1991) Discrete Comput. Geom. , vol.6 , pp. 443-459
    • Bienstock, D.1
  • 36
    • 0017216776 scopus 로고
    • Testing for the consecutive ones property, interval graphs, and planarity using PQ-tree algorithms
    • [BL76]
    • [BL76] Kellogg S. Booth and George S. Lueker. Testing for the consecutive ones property, interval graphs, and planarity using PQ-tree algorithms. J. Computer and System Sciences, 13:335-379, 1976.
    • (1976) J. Computer and System Sciences , vol.13 , pp. 335-379
    • Booth, K.S.1    Lueker, G.S.2
  • 42
    • 0037693146 scopus 로고
    • Scheinerman. Representations of planar graphs
    • [BS93]
    • [BS93] Graham R. Brightwell and Edward R. Scheinerman. Representations of planar graphs. SIAM J. Discrete Math., 6:214-229, 1993.
    • (1993) SIAM J. Discrete Math. , vol.6 , pp. 214-229
    • Brightwell, G.R.1    Edward, R.2
  • 43
    • 84948962268 scopus 로고    scopus 로고
    • Finding Large Planar Subgraphs and Large Subgraphs of a Given Genus
    • [CF96] Jin-Yi Cai and Chak Kuen Wong, editors, Springer-Verlag, Lecture Notes in Computer Science
    • [CF96] Gruia Cǎlinescu and Cristina G. Fernandes. Finding Large Planar Subgraphs and Large Subgraphs of a Given Genus. In Jin-Yi Cai and Chak Kuen Wong, editors, Proceedings 2nd Annual International Conference on Computing and Combinatorics, COCOON'96, pages 152-161. Springer-Verlag, Lecture Notes in Computer Science, vol. 1090, 1996.
    • (1996) Proceedings 2nd Annual International Conference on Computing and Combinatorics, COCOON'96 , vol.1090 , pp. 152-161
    • Cǎlinescu, G.1    Fernandes, C.G.2
  • 45
    • 0041625285 scopus 로고    scopus 로고
    • A Better Approximation Algorithm for Finding Planar Subgraphs
    • [CFFK98]
    • [CFFK98] Gruia Cǎlinescu, Cristina G. Fernandes, Ulrich Finkler, and Howard Karloff. A Better Approximation Algorithm for Finding Planar Subgraphs. J. Algorithms, 27:269-302, 1998.
    • (1998) J. Algorithms , vol.27 , pp. 269-302
    • Cǎlinescu, G.1    Fernandes, C.G.2    Finkler, U.3    Karloff, H.4
  • 47
    • 84947772210 scopus 로고    scopus 로고
    • 5-free Graphs
    • [Che96] Friedhelm Meyer auf der Heide and Burkhard Monien, editors, Springer-Verlag, Lecture Notes in Computer Science
    • 5-free Graphs. In Friedhelm Meyer auf der Heide and Burkhard Monien, editors, Proceedings of the 23rd International Colloquium on Automata, Languages and Programming ICALP'96, pages 269-279. Springer-Verlag, Lecture Notes in Computer Science, vol. 1099, 1996.
    • (1996) Proceedings of the 23rd International Colloquium on Automata, Languages and Programming ICALP'96 , vol.1099 , pp. 269-279
    • Chen, Z.-Z.1
  • 48
    • 0000896863 scopus 로고    scopus 로고
    • 3,3-Free Graphs
    • [Che98]
    • 3,3-Free Graphs. J. Algorithms, 26:166-187, 1998.
    • (1998) J. Algorithms , vol.26 , pp. 166-187
    • Chen, Z.-Z.1
  • 49
    • 0027829965 scopus 로고
    • An O(mlog n)-time algorithm for the maximal planar subgraph problem
    • [CHT93]
    • [CHT93] Leizhen Cai, Xiaofeng Han, and Robert E. Tarjan. An O(mlog n)-time algorithm for the maximal planar subgraph problem. SIAM J. Comput., 22:1142-1162, 1993.
    • (1993) SIAM J. Comput. , vol.22 , pp. 1142-1162
    • Cai, L.1    Han, X.2    Tarjan, R.E.3
  • 51
    • 4043058795 scopus 로고
    • Branch-and-bound techniques for the maximum planar subgraph problem
    • [Cim94]
    • [Cim94] Robert J. Cimikowski. Branch-and-bound techniques for the maximum planar subgraph problem. Intern. J. Computer Math., 53:135-147, 1994.
    • (1994) Intern. J. Computer Math. , vol.53 , pp. 135-147
    • Cimikowski, R.J.1
  • 53
    • 0029343887 scopus 로고
    • On Heuristics for Determining the Thickness of a Graph
    • [Cim95b]
    • [Cim95b] Robert J. Cimikowski. On Heuristics for Determining the Thickness of a Graph. Information Sciences, 85:87-98, 1995.
    • (1995) Information Sciences , vol.85 , pp. 87-98
    • Cimikowski, R.J.1
  • 54
    • 0942281953 scopus 로고    scopus 로고
    • An analysis of heuristics for graph planarization
    • [Cim97]
    • [Cim97] Robert J. Cimikowski. An analysis of heuristics for graph planarization. J. Inf. Optimization Sci., 18:49-73, 1997.
    • (1997) J. Inf. Optimization Sci. , vol.18 , pp. 49-73
    • Cimikowski, R.J.1
  • 55
    • 21144467375 scopus 로고
    • On Assembly of Four-Connected Graphs
    • [CK93] Ernst W. Mayr, editor, Springer-Verlag, Lecture Notes in Computer Science, Extended Abstract
    • [CK93] Jianer Chen and Arkady Kanevsky. On Assembly of Four-Connected Graphs. In Ernst W. Mayr, editor, Proceedings 18th International Workshop on Graph-Theoretic Concepts in Computer Science, WG'92, pages 158-169. Springer-Verlag, Lecture Notes in Computer Science, vol. 657, 1993. Extended Abstract.
    • (1993) Proceedings 18th International Workshop on Graph-Theoretic Concepts in Computer Science, WG'92 , vol.657 , pp. 158-169
    • Chen, J.1    Kanevsky, A.2
  • 57
    • 0002758475 scopus 로고
    • Embedding graphs in books: A layout problem with applications to VLSI design
    • [CLR87]
    • [CLR87] Fan R.K. Chung, Frank Thomson Leighton, and Arnold L. Rosenberg. Embedding graphs in books: A layout problem with applications to VLSI design. SIAM J. Alg. Disc. Meth., 8:33-58, 1987.
    • (1987) SIAM J. Alg. Disc. Meth. , vol.8 , pp. 33-58
    • Chung, F.R.K.1    Leighton, F.T.2    Rosenberg, A.L.3
  • 59
    • 0022010454 scopus 로고
    • A Linear Algorithm for Embedding Planar Graphs Using PQ-Trees
    • [CNAO85]
    • [CNAO85] Norishige Chiba, Takao Nishizeki, Shigenobu Abe, and Takao Ozawa. A Linear Algorithm for Embedding Planar Graphs Using PQ-Trees. J. Computer and System Sciences, 30:54-76, 1985.
    • (1985) J. Computer and System Sciences , vol.30 , pp. 54-76
    • Chiba, N.1    Nishizeki, T.2    Abe, S.3    Ozawa, T.4
  • 63
    • 43949160006 scopus 로고
    • Algorithms for Drawing Graphs: An Annotated Bibliography
    • [DETT94]
    • [DETT94] Giuseppe Di Battista, Peter Eades, Roberto Tamassia, and Ioannis G. Tollis. Algorithms for Drawing Graphs: an Annotated Bibliography. Computational Geometry, 4:235-282, 1994.
    • (1994) Computational Geometry , vol.4 , pp. 235-282
    • Battista, G.D.1    Eades, P.2    Tamassia, R.3    Tollis, I.G.4
  • 65
    • 21444436571 scopus 로고    scopus 로고
    • Planarity and edge poset dimension
    • [dFdM96]
    • [dFdM96] Hubert de Fraysseix and Patrice Ossona de Mendez. Planarity and edge poset dimension. Europ. J. Combinatorics, 17:731-740, 1996.
    • (1996) Europ. J. Combinatorics , vol.17 , pp. 731-740
    • De Fraysseix, H.1    De Mendez, P.O.2
  • 66
    • 0022045717 scopus 로고
    • Analysis of heuristics for finding a maximum weight planar subgraph
    • [DFF85]
    • [DFF85] M.E. Dyer, L.R. Foulds, and A.M. Frieze. Analysis of heuristics for finding a maximum weight planar subgraph. European J. of Operational Research, 20:102-114, 1985.
    • (1985) European J. of Operational Research , vol.20 , pp. 102-114
    • Dyer, M.E.1    Foulds, L.R.2    Frieze, A.M.3
  • 67
    • 0002128850 scopus 로고
    • How to draw a planar graph on a grid
    • [dFPP90]
    • [dFPP90] Hubert de Fraysseix, János Pach, and Richard Pollack. How to draw a planar graph on a grid. Combinatorica, 10:41-51, 1990.
    • (1990) Combinatorica , vol.10 , pp. 41-51
    • De Fraysseix, H.1    Pach, J.2    Pollack, R.3
  • 70
    • 0347964318 scopus 로고
    • A linear algorithm for partitioning graphs of fixed genus
    • [Dji85]
    • [Dji85] Hristo N. Djidjev. A linear algorithm for partitioning graphs of fixed genus. SERDICA Bulgaricae mathematicae publications, 11:369-387, 1985.
    • (1985) SERDICA Bulgaricae Mathematicae Publications , vol.11 , pp. 369-387
    • Djidjev, H.N.1
  • 71
    • 84958050445 scopus 로고
    • A Linear Algorithm for the Maximal Planar Subgraph Problem
    • [Dji95] Selim G. Akl, Frank Dehne, Jörg-Rüdiger Sack, and Nicola Santoro, editors, Springer-Verlag, Lecture Notes in Computer Science
    • [Dji95] Hristo N. Djidjev. A Linear Algorithm for the Maximal Planar Subgraph Problem. In Selim G. Akl, Frank Dehne, Jörg-Rüdiger Sack, and Nicola Santoro, editors, Proceedings 4th International Workshop on Algorithms and Datastructures, WADS'95, pages 369-380. Springer-Verlag, Lecture Notes in Computer Science, vol. 955, 1995.
    • (1995) Proceedings 4th International Workshop on Algorithms and Datastructures, WADS'95 , vol.955 , pp. 369-380
    • Djidjev, H.N.1
  • 76
    • 1542577522 scopus 로고    scopus 로고
    • On-Line Maintenance of Triconnected Components with SPQR-Trees
    • [DT96a]
    • [DT96a] Giuseppe Di Battista and Roberto Tamassia. On-Line Maintenance of Triconnected Components with SPQR-Trees. Algorithmica, 15:302-318, 1996.
    • (1996) Algorithmica , vol.15 , pp. 302-318
    • Battista, G.D.1    Tamassia, R.2
  • 77
    • 0000428115 scopus 로고    scopus 로고
    • On-Line Planarity Testing
    • [DT96b]
    • [DT96b] Giuseppe Di Battista and Roberto Tamassia. On-Line Planarity Testing. SIAM J. Comput., 25(5):956-997, 1996.
    • (1996) SIAM J. Comput. , vol.25 , Issue.5 , pp. 956-997
    • Battista, G.D.1    Tamassia, R.2
  • 78
    • 38249016397 scopus 로고
    • Sur un Nouvel Invariant des Graphes et un Critère de Planarité
    • [dV90]
    • [dV90] Yves Colin de Verdière. Sur un Nouvel Invariant des Graphes et un Critère de Planarité. J. of Combinatorial Theory, Series B, 50:11-21, 1990.
    • (1990) J. of Combinatorial Theory, Series B , vol.50 , pp. 11-21
    • De Verdière, Y.C.1
  • 82
    • 85039491001 scopus 로고
    • [ELMM95] Technical Report DCC-95-15, Departamento de Ciência da Computação, Instituto de Matemaática, Estatística e Ciência da Computação, Universidade Estadual de Campinas, Brazil
    • [ELMM95] Peter Eades, Cláudio L. Lucchesi, João Meidanis, and Candido Ferreira Xavier de Mendonça Neto. NP-hardness Results for Tension-Free Layout. Technical Report DCC-95-15, Departamento de Ciência da Computação, Instituto de Matemaática, Estatística e Ciência da Computação, Universidade Estadual de Campinas, Brazil, 1995.
    • (1995) NP-hardness Results for Tension-Free Layout
    • Eades, P.1    Lucchesi, C.L.2    Meidanis, J.3    De Mendonça Neto, C.F.X.4
  • 83
    • 0142193670 scopus 로고
    • Heuristics for Planarization by Vertex Splitting
    • [EM93] Giuseppe Di Battista, Peter Eades, Hubert de Fraysseix, Pierre Rosenstiehl, and Roberto Tamassia, editors
    • [EM93] Peter Eades and Candido Ferreira Xavier de Mendonça Neto. Heuristics for Planarization by Vertex Splitting. In Giuseppe Di Battista, Peter Eades, Hubert de Fraysseix, Pierre Rosenstiehl, and Roberto Tamassia, editors, ALCOM International Workshop on Graph Drawing, GD'93, Paris, France, September 25-29, 1993, pages 83-85. Available electronically at ftp://ftp.cs.brown.edu/ pub/gd94/gd-92-93/gd93-v2.ps.Z, 1993.
    • (1993) ALCOM International Workshop on Graph Drawing, GD'93, Paris, France, September 25-29, 1993 , pp. 83-85
    • Eades, P.1    De Mendonça Neto, C.F.X.2
  • 84
    • 0142193669 scopus 로고    scopus 로고
    • Vertex Splitting and Tension-Free Layout
    • [EM96] Franz J. Brandenburg, editor, Springer-Verlag, Lecture Notes in Computer Science
    • [EM96] Peter Eades and Candido Ferreira Xavier de Mendonça Neto. Vertex Splitting and Tension-Free Layout. In Franz J. Brandenburg, editor, Graph Drawing. Proceedings of the DIMACS International Workshop, GD'95, pages 202-211. Springer-Verlag, Lecture Notes in Computer Science, vol. 1027, 1996.
    • (1996) Graph Drawing. Proceedings of the DIMACS International Workshop, GD'95 , vol.1027 , pp. 202-211
    • Eades, P.1    De Mendonça Neto, C.F.X.2
  • 88
    • 84947731683 scopus 로고
    • Planarity for Clustered Graphs
    • [FCE95] Paul Spirakis, editor, Springer-Verlag, Lecture Notes in Computer Science
    • [FCE95] Qing-Wen Feng, Robert F. Cohen, and Peter Eades. Planarity for Clustered Graphs. In Paul Spirakis, editor, Third European Symposium on Algorithms, ESA'95, pages 213-226. Springer-Verlag, Lecture Notes in Computer Science, vol. 979, 1995.
    • (1995) Third European Symposium on Algorithms, ESA'95 , vol.979 , pp. 213-226
    • Feng, Q.-W.1    Cohen, R.F.2    Eades, P.3
  • 89
    • 4043051730 scopus 로고    scopus 로고
    • On Eggleton and Guy conjectured upper bound for the crossing number of the n-cube
    • [FF00]
    • [FF00] Luérbio Faria and Celina Miraglia Herrera de Figueiredo. On Eggleton and Guy conjectured upper bound for the crossing number of the n-cube. Math. Slovaca, 50:271-287, 2000.
    • (2000) Math. Slovaca , vol.50 , pp. 271-287
    • Faria, L.1    De Figueiredo, C.M.H.2
  • 91
    • 84949237169 scopus 로고    scopus 로고
    • The Splitting Number of the 4-Cube
    • [FFM98b] Cláudio L. Lucchesi and Arnaldo V. Moura, editors, Springer-Verlag, Lecture Notes in Computer Science
    • [FFM98b] Luérbio Faria, Celina Miraglia Herrera de Figueiredo, and Candido Ferreira Xavier de Mendonça Neto. The Splitting Number of the 4-Cube. In Cláudio L. Lucchesi and Arnaldo V. Moura, editors, Theoretical Informatics. Proceedings of the 3rd Latin American Symposium, LATIN'98, pages 141-150. Springer-Verlag, Lecture Notes in Computer Science, vol. 1380, 1998.
    • (1998) Theoretical Informatics. Proceedings of the 3rd Latin American Symposium, LATIN'98 , vol.1380 , pp. 141-150
    • Faria, L.1    De Figueiredo, C.M.H.2    De Mendonça Neto, C.F.X.3
  • 93
    • 0022128546 scopus 로고
    • Facilities Layout Adjacency Determination: An Experimental Comparison of Three Graph Theoretic Heuristics
    • [FGG85]
    • [FGG85] L.R. Foulds, P.B. Gibbons, and J.W. Giffin. Facilities Layout Adjacency Determination: An Experimental Comparison of Three Graph Theoretic Heuristics. Operations Research, 33:1091-1106, 1985.
    • (1985) Operations Research , vol.33 , pp. 1091-1106
    • Foulds, L.R.1    Gibbons, P.B.2    Giffin, J.W.3
  • 95
    • 4043140918 scopus 로고
    • Minimal Locally Cyclic Triangulations of the Projective Plane
    • [FMN94]
    • [FMN94] Steve Fisk, Bojan Mohar, and Roman Nedela. Minimal Locally Cyclic Triangulations of the Projective Plane. J. of Graph Theory, 18:25-35, 1994.
    • (1994) J. of Graph Theory , vol.18 , pp. 25-35
    • Fisk, S.1    Mohar, B.2    Nedela, R.3
  • 98
    • 0000049494 scopus 로고
    • Greedy randomized adaptive search procedures
    • [FR95]
    • [FR95] T. Feo and Mauricio G.C. Resende. Greedy randomized adaptive search procedures. J. of Global Optimization, 6:109-133, 1995.
    • (1995) J. of Global Optimization , vol.6 , pp. 109-133
    • Feo, T.1    Resende, M.G.C.2
  • 99
    • 84981626646 scopus 로고
    • Algorithms for a Maximum Clique and a Maximum Independent Set of a Circle Graph
    • [Gav73]
    • [Gav73] Fanika Gavril. Algorithms for a Maximum Clique and a Maximum Independent Set of a Circle Graph. Networks, 3:261-273, 1973.
    • (1973) Networks , vol.3 , pp. 261-273
    • Gavril, F.1
  • 100
    • 4043068707 scopus 로고
    • The coarseness of the complete graph
    • [GB68]
    • [GB68] Richard K. Guy and Lowell W. Beineke. The coarseness of the complete graph. Can. J. Math., 20:888-894, 1968.
    • (1968) Can. J. Math. , vol.20 , pp. 888-894
    • Guy, R.K.1    Beineke, L.W.2
  • 101
    • 4043098516 scopus 로고
    • The crossing number of the complement of a circuit
    • [GH73]
    • [GH73] Richard K. Guy and Anthony Hill. The crossing number of the complement of a circuit. Discrete Mathematics, 5:335-344, 1973.
    • (1973) Discrete Mathematics , vol.5 , pp. 335-344
    • Guy, R.K.1    Hill, A.2
  • 104
    • 0000348622 scopus 로고
    • Crossing Number is NPComplete
    • [GJ83]
    • [GJ83] Michael R. Garey and David S. Johnson. Crossing Number is NPComplete. SIAM J. Alg. Disc. Meth., 4:312-316, 1983.
    • (1983) SIAM J. Alg. Disc. Meth. , vol.4 , pp. 312-316
    • Garey, M.R.1    Johnson, D.S.2
  • 109
    • 0004291883 scopus 로고
    • [Grü67] Interscience Publishers, a divsion of John Wiley & Sons
    • [Grü67] Banko Grünbaum. Convex Polytopes. Interscience Publishers, a divsion of John Wiley & Sons, 1967.
    • (1967) Convex Polytopes
    • Grünbaum, B.1
  • 111
    • 21344495886 scopus 로고
    • An efficient graph planarization two-phase heuristic
    • [GT94]
    • [GT94] Oliver Goldschmidt and Alexan Takvorian. An efficient graph planarization two-phase heuristic. Networks, 24:69-73, 1994.
    • (1994) Networks , vol.24 , pp. 69-73
    • Goldschmidt, O.1    Takvorian, A.2
  • 112
    • 38249002109 scopus 로고
    • Planar graphs with no 6-wheel minor
    • [Gub93]
    • [Gub93] Bradley S. Gubser. Planar graphs with no 6-wheel minor. Discrete Mathematics, 120:59-73, 1993.
    • (1993) Discrete Mathematics , vol.120 , pp. 59-73
    • Gubser, B.S.1
  • 114
    • 4043124151 scopus 로고
    • Latest results on crossing numbers
    • [Guy71] Michael Capobianco, Joseph B. Frechen, and M. Krolik, editors, Springer-Verlag, Lecture Notes in Mathematics
    • [Guy71] Richard K. Guy. Latest results on crossing numbers. In Michael Capobianco, Joseph B. Frechen, and M. Krolik, editors, Recent Trends in Graph Theory, Proceedings of the First New York City Graph Theory Conference, June 11-13, 1970, pages 143-156. Springer-Verlag, Lecture Notes in Mathematics, vol. 186, 1971.
    • (1971) Recent Trends in Graph Theory, Proceedings of the First New York City Graph Theory Conference, June 11-13, 1970 , vol.186 , pp. 143-156
    • Guy, R.K.1
  • 115
    • 0010242021 scopus 로고
    • Crossing Numbers of Graphs
    • [Guy72] Y. Alavi, D.R. Lick, and Arthur T. White, editors, Proceedings of the Conference at Western Michigan University, May 10-13, 1972, Springer-Verlag, Lecture Notes in Mathematics
    • [Guy72] Richard K. Guy. Crossing Numbers of Graphs. In Y. Alavi, D.R. Lick, and Arthur T. White, editors, Graph Theory and Applications, pages 111-124. Proceedings of the Conference at Western Michigan University, May 10-13, 1972, Springer-Verlag, Lecture Notes in Mathematics, vol. 303, 1972.
    • (1972) Graph Theory and Applications , vol.303 , pp. 111-124
    • Guy, R.K.1
  • 117
    • 0026147819 scopus 로고
    • On the Thickness of Graphs of Given Degree
    • [Hal91]
    • [Hal91] John H. Halton. On the Thickness of Graphs of Given Degree. Information Sciences, 54:219-238, 1991.
    • (1991) Information Sciences , vol.54 , pp. 219-238
    • Halton, J.H.1
  • 118
    • 0003780715 scopus 로고
    • [Har69] Addison-Wesley Publishing Company
    • [Har69] Frank Harary. Graph theory. Addison-Wesley Publishing Company, 1969.
    • (1969) Graph Theory
    • Harary, F.1
  • 119
    • 4043122704 scopus 로고
    • Bounds on the Coarseness of the n-Cube
    • [Har79]
    • [Har79] Jehuda Hartman. Bounds on the Coarseness of the n-Cube. Canad. Math. Bull., 22:171-175, 1979.
    • (1979) Canad. Math. Bull. , vol.22 , pp. 171-175
    • Hartman, J.1
  • 121
    • 4043105748 scopus 로고
    • The splitting number of the complete graph in the projective plane
    • [Har87]
    • [Har87] Nora Hartsfield. The splitting number of the complete graph in the projective plane. Graphs and Combinatorics, 3:349-356, 1987.
    • (1987) Graphs and Combinatorics , vol.3 , pp. 349-356
    • Hartsfield, N.1
  • 122
    • 0000458503 scopus 로고
    • Map Colour Theorem
    • [Hea90]
    • [Hea90] P.J. Heawood. Map Colour Theorem. Quart. J. Math., 24:332-338, 1890.
    • (1890) Quart. J. Math. , vol.24 , pp. 332-338
    • Heawood, P.J.1
  • 124
    • 0006929466 scopus 로고
    • Embedding outerplanar graphs in small books
    • [Hea87]
    • [Hea87] Lenwood S. Heath. Embedding outerplanar graphs in small books. SIAM J. Alg. Disc. Meth., 8:198-218, 1987.
    • (1987) SIAM J. Alg. Disc. Meth. , vol.8 , pp. 198-218
    • Heath, L.S.1
  • 127
    • 0022937687 scopus 로고
    • A survey of the theory of hypercube graphs
    • [HHW88]
    • [HHW88] Frank Harary, John P. Hayes, and Horng-Jyh Wu. A survey of the theory of hypercube graphs. Comput. Math. Applic., 15:277-289, 1988.
    • (1988) Comput. Math. Applic. , vol.15 , pp. 277-289
    • Harary, F.1    Hayes, J.P.2    Wu, H.-J.3
  • 129
    • 51249171644 scopus 로고
    • The splitting number of the complete graph
    • [HJR85]
    • [HJR85] Nora Hartsfield, Brad Jackson, and Gerhard Ringel. The splitting number of the complete graph. Graphs and Combinatorics, 1:311-329, 1985.
    • (1985) Graphs and Combinatorics , vol.1 , pp. 311-329
    • Hartsfield, N.1    Jackson, B.2    Ringel, G.3
  • 133
    • 4043105747 scopus 로고
    • On a Modified Concept of Thickness of a Graph
    • [HŠ82]
    • [HŠ82] Peter Horák and Jozef Širáň. On a Modified Concept of Thickness of a Graph. Math. Nachr., 108:305-306, 1982.
    • (1982) Math. Nachr. , vol.108 , pp. 305-306
    • Horák, P.1    Širán, J.2
  • 134
    • 4043143719 scopus 로고
    • A construction of thickness-minimal graphs
    • [HŠ87]
    • [HŠ87] Peter Horák and Jozef Širáň. A construction of thickness-minimal graphs. Discrete Mathematics, 64:263-268, 1987.
    • (1987) Discrete Mathematics , vol.64 , pp. 263-268
    • Horák, P.1    Širáň, J.2
  • 135
    • 84955561847 scopus 로고
    • A linear time algorithm for finding maximal planar subgraphs
    • [Hsu95] John Staples, Peter Eades, Naoki Katoh, and Alistair Moffat, editors, Springer-Verlag, Lecture Notes in Computer Science
    • [Hsu95] Wen-Lian Hsu. A linear time algorithm for finding maximal planar subgraphs. In John Staples, Peter Eades, Naoki Katoh, and Alistair Moffat, editors, Algorithms and Computation, 6th International Symposium, ISAAC'95, pages 352-361. Springer-Verlag, Lecture Notes in Computer Science, vol. 1004, 1995.
    • (1995) Algorithms and Computation, 6th International Symposium, ISAAC'95 , vol.1004 , pp. 352-361
    • Hsu, W.-L.1
  • 136
    • 84947928171 scopus 로고    scopus 로고
    • On Representations of Some Thickness-Two Graphs
    • [HSV96] Franz J. Brandenburg, editor, Springer-Verlag, Lecture Notes in Computer Science
    • [HSV96] Joan P. Hutchinson, Thomas Shermer, and Andrew Vince. On Representations of Some Thickness-Two Graphs. In Franz J. Brandenburg, editor, Graph Drawing. Proceedings of the DIMACS International Workshop, GD'95, pages 324-332. Springer-Verlag, Lecture Notes in Computer Science, vol. 1027, 1996.
    • (1996) Graph Drawing. Proceedings of the DIMACS International Workshop, GD'95 , vol.1027 , pp. 324-332
    • Hutchinson, J.P.1    Shermer, T.2    Vince, A.3
  • 137
    • 0042709989 scopus 로고    scopus 로고
    • On representations of some thickness-two graphs
    • [HSV99]
    • [HSV99] Joan P. Hutchinson, Thomas Shermer, and Andrew Vince. On representations of some thickness-two graphs. Computational Geometry, 13:161-171, 1999.
    • (1999) Computational Geometry , vol.13 , pp. 161-171
    • Hutchinson, J.P.1    Shermer, T.2    Vince, A.3
  • 138
    • 0012916439 scopus 로고
    • A dual form of Kuratowski's theorem
    • [HT65]
    • [HT65] Frank Harary and William T. Tutte. A dual form of Kuratowski's theorem. Canad. Math. Bull., 8:17-20, 1965.
    • (1965) Canad. Math. Bull. , vol.8 , pp. 17-20
    • Harary, F.1    Tutte, W.T.2
  • 141
    • 84957352759 scopus 로고    scopus 로고
    • Pitfalls of Using PQ-Trees in Automatic Graph Drawing
    • [JLM97] Giuseppe Di Battista, editor, Springer-Verlag, Lecture Notes in Computer Science
    • [JLM97] Michael Jünger, Sebastian Leipert, and Petra Mutzel. Pitfalls of Using PQ-Trees in Automatic Graph Drawing. In Giuseppe Di Battista, editor, Proceedings of the Symposium on Graph Drawing, GD'97, pages 193-204. Springer-Verlag, Lecture Notes in Computer Science, vol. 1353, 1997.
    • (1997) Proceedings of the Symposium on Graph Drawing, GD'97 , vol.1353 , pp. 193-204
    • Jünger, M.1    Leipert, S.2    Mutzel, P.3
  • 142
    • 84957360737 scopus 로고    scopus 로고
    • A Polyhedral Approach to the Multi-Layer Crossing Minimization Problem
    • [JLMO97] Giuseppe Di Battista, editor, Springer-Verlag, Lecture Notes in Computer Science
    • [JLMO97] Michael Jünger, Eva K. Lee, Petra Mutzel, and Thomas Odenthal. A Polyhedral Approach to the Multi-Layer Crossing Minimization Problem. In Giuseppe Di Battista, editor, Proceedings of the Symposium on Graph Drawing, GD'97, pages 13-24. Springer-Verlag, Lecture Notes in Computer Science, vol. 1353, 1997.
    • (1997) Proceedings of the Symposium on Graph Drawing, GD'97 , vol.1353 , pp. 13-24
    • Jünger, M.1    Lee, E.K.2    Mutzel, P.3    Odenthal, T.4
  • 143
    • 0002066416 scopus 로고    scopus 로고
    • Maximum Planar Subgraphs and Nice Embeddings: Practical Layout Tools
    • [JM96]
    • [JM96] Michael Jünger and Petra Mutzel. Maximum Planar Subgraphs and Nice Embeddings: Practical Layout Tools. Algorithmica, 16:33-59, 1996.
    • (1996) Algorithmica , vol.16 , pp. 33-59
    • Jünger, M.1    Mutzel, P.2
  • 144
    • 0002468332 scopus 로고    scopus 로고
    • 2-Layer Straightline Crossing Minimization: Performance of Exact and Heuristic Algorithms
    • [JM97]
    • [JM97] Michael Jünger and Petra Mutzel. 2-Layer Straightline Crossing Minimization: Performance of Exact and Heuristic Algorithms. Journal of Graph Algorithms and Applications, 1:1-25, 1997.
    • (1997) Journal of Graph Algorithms and Applications , vol.1 , pp. 1-25
    • Jünger, M.1    Mutzel, P.2
  • 145
    • 85137966604 scopus 로고
    • [JMOS94] Technical Report 94.168, Universität zu Köln
    • 5-Minors. Technical Report 94.168, Universität zu Köln, 1994. Available electronically at ftp://ftp.ZPR.unikoeln. de/pub/paper/zpr94-168.ps.gz.
    • (1994) 5-Minors
    • Jünger, M.1    Mutzel, P.2    Odenthal, T.3    Scharbrodt, M.4
  • 146
    • 0004535247 scopus 로고    scopus 로고
    • The Thickness of a Minor-Excluded Class of Graphs
    • [JMOS98]
    • [JMOS98] Michael Jünger, Petra Mutzel, Thomas Odenthal, and Mark Scharbrodt. The Thickness of a Minor-Excluded Class of Graphs. Discrete Mathematics, 182:169-176, 1998.
    • (1998) Discrete Mathematics , vol.182 , pp. 169-176
    • Jünger, M.1    Mutzel, P.2    Odenthal, T.3    Scharbrodt, M.4
  • 147
    • 46549091823 scopus 로고
    • The NP-Completeness Column: An Ongoing Guide
    • [Joh85]
    • [Joh85] David S. Johnson. The NP-Completeness Column: An Ongoing Guide. J. Algorithms, 6:434-451, 1985.
    • (1985) J. Algorithms , vol.6 , pp. 434-451
    • Johnson, D.S.1
  • 148
    • 4043053130 scopus 로고
    • Plane constructions for graphs, networks, and maps measurements of planarity
    • [JR84a] Springer-Verlag, Lecture Notes in Economics and Mathematical Systems
    • [JR84a] Brad Jackson and Gerhard Ringel. Plane constructions for graphs, networks, and maps measurements of planarity. In Selected topics in operations research and mathematical economics, Proc. 8th Symp., Karlsruhe 1983, pages 315-324. Springer-Verlag, Lecture Notes in Economics and Mathematical Systems, vol. 226, 1984.
    • (1984) Selected Topics in Operations Research and Mathematical Economics, Proc. 8th Symp., Karlsruhe 1983 , vol.226 , pp. 315-324
    • Jackson, B.1    Ringel, G.2
  • 149
    • 0142162792 scopus 로고
    • The splitting number of complete bipartite graphs
    • [JR84b]
    • [JR84b] Brad Jackson and Gerhard Ringel. The splitting number of complete bipartite graphs. Arch. Math., 42:178-184, 1984.
    • (1984) Arch. Math. , vol.42 , pp. 178-184
    • Jackson, B.1    Ringel, G.2
  • 162
    • 0043209532 scopus 로고
    • Node-deletion NP-complete problems
    • [KD79]
    • [KD79] M.S. Krishnamoorthy and Narsingh Deo. Node-deletion NP-complete problems. SIAM J. Comput., 8:619-625, 1979.
    • (1979) SIAM J. Comput. , vol.8 , pp. 619-625
    • Krishnamoorthy, M.S.1    Deo, N.2
  • 164
    • 0001872985 scopus 로고
    • An Analysis of the Greedy Heuristic for Independence Systems
    • [KH78] Brian R. Alspach, editor, North-Holland, Annals of Discrete Mathematics
    • [KH78] Bernhard Korte and Dirk Hausmann. An Analysis of the Greedy Heuristic for Independence Systems. In Brian R. Alspach, editor, Algorithmic Aspects of Combinatorics, pages 65-74. North-Holland, Annals of Discrete Mathematics, vol. 2, 1978.
    • (1978) Algorithmic Aspects of Combinatorics , vol.2 , pp. 65-74
    • Korte, B.1    Hausmann, D.2
  • 166
    • 84864590690 scopus 로고
    • On the problem of skew curves in topology
    • [KJ83] M. Borowiecki, J.W. Kennedy, and Maciej M. Sysło, editors, Springer-Verlag, Lecture Notes in Mathematics, Translation of [Kur30] by Jan Jaworowski.
    • [KJ83] Kazimierz Kuratowski and Jan Jaworowski. On the problem of skew curves in topology. In M. Borowiecki, J.W. Kennedy, and Maciej M. Sysło, editors, Graph Theory, Proc. of a Conference held in Łagów, Poland, February 10-13, 1981, pages 1-13. Springer-Verlag, Lecture Notes in Mathematics, vol. 1018, 1983. Translation of [Kur30] by Jan Jaworowski.
    • (1983) Graph Theory, Proc. of a Conference Held in Łagów, Poland, February 10-13, 1981 , vol.1018 , pp. 1-13
    • Kuratowski, K.1    Jaworowski, J.2
  • 167
    • 4043054553 scopus 로고
    • Die Dicke des n-dimensionalen Würfel-Graphen
    • [Kle67]
    • [Kle67] Michael Kleinert. Die Dicke des n-dimensionalen Würfel-Graphen. J. of Combinatorial Theory, 3:10-15, 1967.
    • (1967) J. of Combinatorial Theory , vol.3 , pp. 10-15
    • Kleinert, M.1
  • 169
    • 0346478465 scopus 로고
    • On the crossing numbers of Cartesian products of stars and paths or cycles
    • [Kle91]
    • [Kle91] Marián Klešč. On the crossing numbers of Cartesian products of stars and paths or cycles. Math. Slovaca, 41(2):113-120, 1991.
    • (1991) Math. Slovaca , vol.41 , Issue.2 , pp. 113-120
    • Klešč, M.1
  • 170
    • 84987553942 scopus 로고
    • The Crossing Numbers of Products of Paths and Stars with 4-Vertex Graphs
    • [Kle94]
    • [Kle94] Marián Klešč. The Crossing Numbers of Products of Paths and Stars with 4-Vertex Graphs. J. of Graph Theory, 18:605-614, 1994.
    • (1994) J. of Graph Theory , vol.18 , pp. 605-614
    • Klešč, M.1
  • 171
    • 0347739139 scopus 로고
    • The crossing numbers of certain Cartesian products
    • [Kle95]
    • [Kle95] Marián Klešč. The crossing numbers of certain Cartesian products. Discussiones Mathematicae - Graph Theory, 15:5-10, 1995.
    • (1995) Discussiones Mathematicae - Graph Theory , vol.15 , pp. 5-10
    • Klešč, M.1
  • 174
    • 38249035104 scopus 로고
    • Construction of crossing-critical graphs
    • [Koc87]
    • [Koc87] Martin Kochol. Construction of crossing-critical graphs. Discrete Mathematics, 66:311-313, 1987.
    • (1987) Discrete Mathematics , vol.66 , pp. 311-313
    • Kochol, M.1
  • 175
    • 85039496601 scopus 로고
    • Linear Jump of Crossing Number for Non Kuratowski Edge of a Graph
    • [Koc91]
    • [Koc91] Martin Kochol. Linear Jump of Crossing Number for Non Kuratowski Edge of a Graph. Radovi Matematicki, 7:177-184, 1991.
    • (1991) Radovi Matematicki , vol.7 , pp. 177-184
    • Kochol, M.1
  • 177
    • 0041758585 scopus 로고
    • [Kön90] Birkhäuser, Originally published in 1936 as Theorie der endlichen und unendlichen Graphen. With a commentary by William T. Tutte.
    • [Kön90] Dénes König. Theory of Finite and Infinite Graphs. Birkhäuser, 1990. Originally published in 1936 as Theorie der endlichen und unendlichen Graphen. With a commentary by William T. Tutte.
    • (1990) Theory of Finite and Infinite Graphs
    • König, D.1
  • 179
    • 0000157130 scopus 로고
    • Sur le problème des courbes gauches en topologie
    • [Kur30]
    • [Kur30] Kazimierz Kuratowski. Sur le problème des courbes gauches en topologie. Fundamenta Mathematicae, 15:271-283, 1930.
    • (1930) Fundamenta Mathematicae , vol.15 , pp. 271-283
    • Kuratowski, K.1
  • 180
    • 0011655829 scopus 로고
    • On Stable Crossing Numbers
    • [KW78]
    • [KW78] Paul C. Kainen and Arthur T. White. On Stable Crossing Numbers. J. of Graph Theory, 2:181-187, 1978.
    • (1978) J. of Graph Theory , vol.2 , pp. 181-187
    • Kainen, P.C.1    White, A.T.2
  • 182
  • 183
    • 0002659740 scopus 로고
    • Graph Algorithms
    • [Lee90] Jan v. Leeuwen, editor, Algorithms and Complexity, Elsevier Science Pub., Amsterdam
    • [Lee90] Jan v. Leeuwen. Graph Algorithms. In Jan v. Leeuwen, editor, Algorithms and Complexity, volume A of Handbook of Theoretical Computer Science, pages 525-631. Elsevier Science Pub., Amsterdam, 1990.
    • (1990) Handbook of Theoretical Computer Science , vol.A , pp. 525-631
    • Leeuwen, J.V.1
  • 186
    • 0002621814 scopus 로고
    • New Lower Bound Techniques for VLSI
    • [Lei84]
    • [Lei84] Frank Thomson Leighton. New Lower Bound Techniques for VLSI. Math. Systems Theory, 17:47-70, 1984.
    • (1984) Math. Systems Theory , vol.17 , pp. 47-70
    • Leighton, F.T.1
  • 189
    • 0000042272 scopus 로고
    • A new graph-theoretic heuristic for facility layout
    • [Leu92]
    • [Leu92] Janny Leung. A new graph-theoretic heuristic for facility layout. Management Science, 38:594-605, 1992.
    • (1992) Management Science , vol.38 , pp. 594-605
    • Leung, J.1
  • 191
    • 0002794707 scopus 로고
    • Planar Formulae and their Uses
    • [Lic82]
    • [Lic82] D. Lichtenstein. Planar Formulae and their Uses. SIAM J. Comput., 11:329-343, 1982.
    • (1982) SIAM J. Comput. , vol.11 , pp. 329-343
    • Lichtenstein, D.1
  • 192
    • 0019001812 scopus 로고
    • The Node-Deletion Problem for Hereditary Properties is NP-Complete
    • [LY80]
    • [LY80] John M. Lewis and Mihalis Yannakakis. The Node-Deletion Problem for Hereditary Properties is NP-Complete. J. Computer and System Sciences, 20:219-230, 1980.
    • (1980) J. Computer and System Sciences , vol.20 , pp. 219-230
    • Lewis, J.M.1    Yannakakis, M.2
  • 193
    • 0041806818 scopus 로고
    • A combinatorial condition for planar graphs
    • [Mac37]
    • [Mac37] S. MacLane. A combinatorial condition for planar graphs. Fundamenta Mathematicae, 28:22-32, 1937.
    • (1937) Fundamenta Mathematicae , vol.28 , pp. 22-32
    • MacLane, S.1
  • 194
    • 0011677948 scopus 로고
    • Bounds for the Crossing Number of the N-Cube
    • [Mad91]
    • [Mad91] Tom Madej. Bounds for the Crossing Number of the N-Cube. J. of Graph Theory, 15:81-97, 1991.
    • (1991) J. of Graph Theory , vol.15 , pp. 81-97
    • Madej, T.1
  • 195
    • 0346834702 scopus 로고
    • Graphs with e Edges Have Pagenumber O(√E)
    • [Mal94]
    • [Mal94] Seth M. Malitz. Graphs with E Edges Have Pagenumber O(√E). J. Algorithms, 17:71-84, 1994.
    • (1994) J. Algorithms , vol.17 , pp. 71-84
    • Malitz, S.M.1
  • 196
    • 84975969582 scopus 로고
    • Determining the thickness of graphs is NP-hard
    • [Man83]
    • [Man83] Anthony Mansfield. Determining the thickness of graphs is NP-hard. Math. Proc. Camb. Phil. Soc., 93:9-23, 1983.
    • (1983) Math. Proc. Camb. Phil. Soc. , vol.93 , pp. 9-23
    • Mansfield, A.1
  • 197
    • 85039499254 scopus 로고    scopus 로고
    • [ME93a] Genetic Algorithms For Vertex Splitting in DAGs. Technical Report CSC-93-02, Computer Science Department, University of Missouri-Rolla, MO 65401, USA, January 1993. Presented as a poster
    • [ME93a] Matthias Mayer and Fikret Ercal. Genetic Algorithms For Vertex Splitting in DAGs. Technical Report CSC-93-02, Computer Science Department, University of Missouri-Rolla, MO 65401, USA, January 1993. Presented as a poster at The Fifth Int'l Conf. on Genetic Algorithms (ICGA-93). Available electronically at http://www.cs.umr.edu/techrpt/postscript/93-02.ps.
    • The Fifth Int'l Conf. on Genetic Algorithms (ICGA-93)
    • Mayer, M.1    Ercal, F.2
  • 198
    • 4043115757 scopus 로고
    • [ME93b] Technical Report CSC-93-10, Computer Science Department, University of Missouri-Rolla, MO 65401, USA, May
    • [ME93b] Matthias Mayer and Fikret Ercal. Parallel Genetic Algorithms For the DAG Vertex Splitting Problem. Technical Report CSC-93-10, Computer Science Department, University of Missouri-Rolla, MO 65401, USA, May 1993.
    • (1993) Parallel Genetic Algorithms for the DAG Vertex Splitting Problem
    • Mayer, M.1    Ercal, F.2
  • 200
    • 0142255867 scopus 로고
    • [Men94] PhD thesis, University of Queensland, Australia, March Technical Report No. 94-01, Department of Computer Science, The University of Newcastle, Australia.
    • [Men94] Candido Ferreira Xavier de Mendonça Neto. A Layout System for Information System Diagrams. PhD thesis, University of Queensland, Australia, March 1994. Technical Report No. 94-01, Department of Computer Science, The University of Newcastle, Australia.
    • (1994) A Layout System for Information System Diagrams
    • De Mendonça Neto, C.F.X.1
  • 201
    • 84858271177 scopus 로고
    • On middle and total graphs with coarseness number equal 1
    • [Mic83] M. Borowiecki, J.W. Kennedy, and Maciej M. Sysło, editors, Springer-Verlag, Lecture Notes in Mathematics
    • [Mic83] Danuta Michalak. On middle and total graphs with coarseness number equal 1. In M. Borowiecki, J.W. Kennedy, and Maciej M. Sysło, editors, Graph Theory, Proc. of a Conference held in Łagów, Poland, February 10-13, 1981, pages 139-150. Springer-Verlag, Lecture Notes in Mathematics, vol. 1018, 1983.
    • (1983) Graph Theory, Proc. of a Conference Held in Łagów, Poland, February 10-13, 1981 , vol.1018 , pp. 139-150
    • Michalak, D.1
  • 203
    • 84986495445 scopus 로고
    • Pagenumber of Complete Bipartite Graphs
    • [MLW88]
    • [MLW88] Douglas Muder, Margaret Lefevre Weaver, and Douglas B. West. Pagenumber of Complete Bipartite Graphs. J. of Graph Theory, 12:469-489, 1988.
    • (1988) J. of Graph Theory , vol.12 , pp. 469-489
    • Muder, D.1    Weaver, M.L.2    West, D.B.3
  • 204
    • 38249008557 scopus 로고
    • Generating locally-cyclic triangulations of surfaces
    • [MM92]
    • [MM92] Aleksander Malnič and Bojan Mohar. Generating locally-cyclic triangulations of surfaces. J. of Combinatorial Theory, Series B, 56:147-164, 1992.
    • (1992) J. of Combinatorial Theory, Series B , vol.56 , pp. 147-164
    • Malnič, A.1    Mohar, B.2
  • 205
    • 0005316925 scopus 로고    scopus 로고
    • On the Embedding Phase of the Hopcroft and Tarjan Planarity Testing Algorithm
    • [MM96]
    • [MM96] Kurt Mehlhorn and Petra Mutzel. On the Embedding Phase of the Hopcroft and Tarjan Planarity Testing Algorithm. Algorithmica, 16:233-242, 1996.
    • (1996) Algorithmica , vol.16 , pp. 233-242
    • Mehlhorn, K.1    Mutzel, P.2
  • 206
    • 1542500413 scopus 로고
    • [MMN93] Technical Report MPI-I-93-151, Max-Planck-Institut für Informatik, Im Stadtwald, 66123 Saarbrücken, Germany
    • [MMN93] Kurt Mehlhorn, Petra Mutzel, and Stefan Näher. An Implementation of the Hopcroft and Tarjan Planarity Test and Embedding Algorithm. Technical Report MPI-I-93-151, Max-Planck-Institut für Informatik, Im Stadtwald, 66123 Saarbrücken, Germany, 1993. Available electronically at http://www.mpi-sb.mpg.de/~mutzel/mpireports/MPI-I-93-151.ps. gz.
    • (1993) An Implementation of the Hopcroft and Tarjan Planarity Test and Embedding Algorithm
    • Mehlhorn, K.1    Mutzel, P.2    Näher, S.3
  • 210
    • 85137963495 scopus 로고
    • [MP95] Technical report, Technion - Israel Institute of Technology, September
    • 3,3-free Graphs. Technical report, Technion - Israel Institute of Technology, September 1995.
    • (1995) 3,3-free Graphs
    • Manor, R.1    Penn, M.2
  • 211
    • 0001572279 scopus 로고
    • On the crossing numbers of certain generalized Petersen graphs
    • [MR92]
    • [MR92] Dan McQuillan and R. Bruce Richter. On the crossing numbers of certain generalized Petersen graphs. Discrete Mathematics, 104:311-320, 1992.
    • (1992) Discrete Mathematics , vol.104 , pp. 311-320
    • McQuillan, D.1    Bruce Richter, R.2
  • 212
    • 84987566749 scopus 로고
    • On 3-Regular Graphs Having Crossing Number at least 2
    • [MR94]
    • [MR94] Dan McQuillan and R. Bruce Richter. On 3-Regular Graphs Having Crossing Number at least 2. J. of Graph Theory, 18:831-839, 1994.
    • (1994) J. of Graph Theory , vol.18 , pp. 831-839
    • McQuillan, D.1    Bruce Richter, R.2
  • 213
    • 0040103223 scopus 로고    scopus 로고
    • [Mut94] PhD thesis, Universität zu Köln, 1994. The Introduction and the Table of Contents are available electronically
    • [Mut94] Petra Mutzel. The Maximum Planar Subgraph Problem. PhD thesis, Universität zu Köln, 1994. The Introduction and the Table of Contents are available electronically at http://www.mpisb.mpg.de/~mutzel/koelnreports/.
    • The Maximum Planar Subgraph Problem
    • Mutzel, P.1
  • 215
    • 84864598718 scopus 로고
    • Planar graph problems
    • [Nis90] Gottfried Tinhofer, Ernst W. Mayr, Hartmut Noltemeier, and Maciej M. Sysło, editors, Springer-Verlag Wien New York
    • [Nis90] Takao Nishizeki. Planar graph problems. In Gottfried Tinhofer, Ernst W. Mayr, Hartmut Noltemeier, and Maciej M. Sysło, editors, Computational Graph Theory, volume 7 of Computing Supplementum, pages 53-68. Springer-Verlag Wien New York, 1990.
    • (1990) Computational Graph Theory, Volume 7 of Computing Supplementum , pp. 53-68
    • Nishizeki, T.1
  • 216
    • 85137967596 scopus 로고
    • [NP94] Technical report, Technion - Israel Institute of Technology, June
    • 3,3-free Digraphs. Technical report, Technion - Israel Institute of Technology, June 1994.
    • (1994) 3,3-free Digraphs
    • Nutov, Z.1    Penn, M.2
  • 218
    • 0013536055 scopus 로고
    • Connected detachments of graphs and generalized Euler trails
    • [NW85a]
    • [NW85a] Crispin St.J.A. Nash-Williams. Connected detachments of graphs and generalized Euler trails. J. London Math. Soc. (2), 31:17-29, 1985.
    • (1985) J. London Math. Soc. , vol.31 , Issue.2 , pp. 17-29
    • Nash-Williams, C.St.J.A.1
  • 219
    • 0001766092 scopus 로고
    • Detachments of graphs and generalised Euler trails
    • [NW85b] Ian Anderson, editor, Surveys in Combinatorics 1985, Pap. 10th British Combinatorial Conference, Glasgow, Scotland, 1985, Cambridge Univ. Press, Cambridge-New York
    • [NW85b] Crispin St.J.A. Nash-Williams. Detachments of graphs and generalised Euler trails. In Ian Anderson, editor, Surveys in Combinatorics 1985, Pap. 10th British Combinatorial Conference, Glasgow, Scotland, 1985, volume 103 of London Mathematical Society Lecture Note Series, pages 137-151. Cambridge Univ. Press, Cambridge-New York, 1985.
    • (1985) London Mathematical Society Lecture Note Series , vol.103 , pp. 137-151
    • Nash-Williams, C.St.J.A.1
  • 220
    • 38249033543 scopus 로고
    • Amalgamations of almost regular edge-colourings of simple graphs
    • [NW87]
    • [NW87] Crispin St.J.A. Nash-Williams. Amalgamations of almost regular edge-colourings of simple graphs. J. of Combinatorial Theory, Series B, 43:322-342, 1987.
    • (1987) J. of Combinatorial Theory, Series B , vol.43 , pp. 322-342
    • Nash-Williams, C.St.J.A.1
  • 221
    • 0345015240 scopus 로고
    • Embedding de Bruijn and shue-exchange graphs in five pages
    • [Obr93]
    • [Obr93] Bojana Obrenić. Embedding de Bruijn and shue-exchange graphs in five pages. SIAM J. Discrete Math., 6:642-654, 1993.
    • (1993) SIAM J. Discrete Math. , vol.6 , pp. 642-654
    • Obrenić, B.1
  • 222
    • 84864593343 scopus 로고
    • [Ode94] Master's thesis, Institut für Informatik, Universität zu Köln
    • [Ode94] Thomas Odenthal. Die Schichtzahl von Graphen. Master's thesis, Institut für Informatik, Universität zu Köln, 1994.
    • (1994) Die Schichtzahl Von Graphen
    • Odenthal, T.1
  • 226
    • 4043129765 scopus 로고
    • On the Factor-Thickness of Regular Graphs
    • [PCK89]
    • [PCK89] Y.H. Peng, C.C. Chen, and K.M. Koh. On the Factor-Thickness of Regular Graphs. Graphs and Combinatorics, 5:173-188, 1989.
    • (1989) Graphs and Combinatorics , vol.5 , pp. 173-188
    • Peng, Y.H.1    Chen, C.C.2    Koh, K.M.3
  • 229
    • 1542501882 scopus 로고    scopus 로고
    • Applications of the Crossing Number
    • [PSS96]
    • [PSS96] János Pach, Farhad Shahrokhi, and Mario Szegedy. Applications of the Crossing Number. Algorithmica, 16:111-117, 1996.
    • (1996) Algorithmica , vol.16 , pp. 111-117
    • Pach, J.1    Shahrokhi, F.2    Szegedy, M.3
  • 230
    • 0031455815 scopus 로고    scopus 로고
    • Graphs drawn with few crossings per edge
    • [PT97]
    • [PT97] János Pach and Géza Tóth. Graphs drawn with few crossings per edge. Combinatorica, 17:427-439, 1997.
    • (1997) Combinatorica , vol.17 , pp. 427-439
    • Pach, J.1    Tóth, G.2
  • 233
    • 84986471233 scopus 로고
    • Cubic Graphs with Crossing Number Two
    • [Ric88]
    • [Ric88] R. Bruce Richter. Cubic Graphs with Crossing Number Two. J. of Graph Theory, 12:363-374, 1988.
    • (1988) J. of Graph Theory , vol.12 , pp. 363-374
    • Bruce Richter, R.1
  • 234
    • 0042143483 scopus 로고
    • Die toroidale Dicke des vollständigen Graphen
    • [Rin65]
    • [Rin65] Gerhard Ringel. Die toroidale Dicke des vollständigen Graphen. Math. Z., 87:19-26, 1965.
    • (1965) Math. Z. , vol.87 , pp. 19-26
    • Ringel, G.1
  • 236
    • 0027574594 scopus 로고
    • Scheduling algorithms for multihop radio networks
    • [RL93]
    • [RL93] Subramanian Ramanathan and Errol L. Lloyd. Scheduling algorithms for multihop radio networks. IEEE/ACM Transactions on Networking, 1:166-177, 1993.
    • (1993) IEEE/ACM Transactions on Networking , vol.1 , pp. 166-177
    • Ramanathan, S.1    Lloyd, E.L.2
  • 237
    • 0043161651 scopus 로고    scopus 로고
    • The Vertex-Disjoint Menger Problem in Planar Graphs
    • [RLWW97]
    • [RLWW97] Heike Ripphausen-Lipa, Dorothea Wagner, and Karsten Weihe. The Vertex-Disjoint Menger Problem in Planar Graphs. SIAM J. Comput., 26:331-349, 1997.
    • (1997) SIAM J. Comput. , vol.26 , pp. 331-349
    • Ripphausen-Lipa, H.1    Wagner, D.2    Weihe, K.3
  • 238
    • 0039325578 scopus 로고    scopus 로고
    • A GRASP for Graph Planarization
    • [RR97]
    • [RR97] Mauricio G.C. Resende and Celso C. Ribeiro. A GRASP for Graph Planarization. Networks, 29:173-189, 1997.
    • (1997) Networks , vol.29 , pp. 173-189
    • Resende, M.G.C.1    Ribeiro, C.C.2
  • 241
    • 0002859647 scopus 로고    scopus 로고
    • A new proof of the four-colour theorem
    • [RSST96]
    • [RSST96] Neil Robertson, Daniel P. Sanders, Paul Seymour, and Robin Thomas. A new proof of the four-colour theorem. ERA Amer. Math. Soc., 2(1):17-25, 1996. Available electronically at http://www.ams.org/era/1996-02-01/ .
    • (1996) ERA Amer. Math. Soc. , vol.2 , Issue.1 , pp. 17-25
    • Robertson, N.1    Sanders, D.P.2    Seymour, P.3    Thomas, R.4
  • 242
    • 0022162361 scopus 로고
    • A note on finding minimum-cost edge-disjoint spanning trees
    • [RT85]
    • [RT85] J. Roskind and Robert E. Tarjan. A note on finding minimum-cost edge-disjoint spanning trees. Mathematics of Operations Research, 10:701-708, 1985.
    • (1985) Mathematics of Operations Research , vol.10 , pp. 701-708
    • Roskind, J.1    Tarjan, R.E.2
  • 245
    • 0031504393 scopus 로고    scopus 로고
    • Relations between Crossing Numbers of Complete and Complete Bipartite Graphs
    • [RT97]
    • [RT97] R. Bruce Richter and Carsten Thomassen. Relations Between Crossing Numbers of Complete and Complete Bipartite Graphs. The American Mathematical Monthly, 104:131-137, 1997.
    • (1997) The American Mathematical Monthly , vol.104 , pp. 131-137
    • Bruce Richter, R.1    Thomassen, C.2
  • 247
    • 85039488197 scopus 로고
    • A parallel approximate algorithm for minimum edge deletion bipartite subgraph problem
    • [SC89]
    • [SC89] Ranjan Kumar Sen and Pranay Chaudhuri. A parallel approximate algorithm for minimum edge deletion bipartite subgraph problem. J. of Combinatorics, Information & System Sciences, 14:111-123, 1989.
    • (1989) J. of Combinatorics, Information & System Sciences , vol.14 , pp. 111-123
    • Sen, R.K.1    Chaudhuri, P.2
  • 249
    • 0039719277 scopus 로고
    • Planar Graphs and Poset Dimension
    • [Sch89]
    • [Sch89] Walter Schnyder. Planar Graphs and Poset Dimension. Order, 5:323-343, 1989.
    • (1989) Order , vol.5 , pp. 323-343
    • Schnyder, W.1
  • 253
    • 84864603954 scopus 로고
    • [Sch95] Master's thesis, Institut für Informatik, Universität zu Köln
    • [Sch95] Mark Scharbrodt. Die Kreuzungszahl von Graphen. Master's thesis, Institut für Informatik, Universität zu Köln, 1995.
    • (1995) Die Kreuzungszahl Von Graphen
    • Scharbrodt, M.1
  • 255
    • 0023964502 scopus 로고
    • Split vertices in vertex colouring and their application in developing a solution to the faculty timetable problem
    • [Sel88]
    • [Sel88] S.M. Selim. Split vertices in vertex colouring and their application in developing a solution to the faculty timetable problem. The Computer Journal, 31(1):76-82, 1988.
    • (1988) The Computer Journal , vol.31 , Issue.1 , pp. 76-82
    • Selim, S.M.1
  • 259
    • 0010232210 scopus 로고
    • Crossing-critical edges and Kuratowski subgraphs of a graph
    • [Šir83]
    • [Šir83] Jozef Širáň. Crossing-critical edges and Kuratowski subgraphs of a graph. J. of Combinatorial Theory, Series B, 35:83-92, 1983.
    • (1983) J. of Combinatorial Theory, Series B , vol.35 , pp. 83-92
    • Širáň, J.1
  • 260
    • 0041961885 scopus 로고
    • Infinite families of crossing-critical graphs with a given crossing number
    • [Šir84]
    • [Šir84] Jozef Širáň. Infinite families of crossing-critical graphs with a given crossing number. Discrete Mathematics, 48:129-132, 1984.
    • (1984) Discrete Mathematics , vol.48 , pp. 129-132
    • Širáň, J.1
  • 262
    • 0013016112 scopus 로고
    • A Classification of 4-Connected Graphs
    • [Sla74]
    • [Sla74] Peter J. Slater. A Classification of 4-Connected Graphs. J. of Combinatorial Theory, Series B, 17:281-298, 1974.
    • (1974) J. of Combinatorial Theory, Series B , vol.17 , pp. 281-298
    • Slater, P.J.1
  • 265
    • 84974122218 scopus 로고
    • On Canonical Concurrent Flows, Crossing Number and Graph Expansion
    • [SS94]
    • [SS94] Farhad Shahrokhi and László A. Székely. On Canonical Concurrent Flows, Crossing Number and Graph Expansion. Combinatorics, Probability and Computing, 3:523-543, 1994.
    • (1994) Combinatorics, Probability and Computing , vol.3 , pp. 523-543
    • Shahrokhi, F.1    Székely, L.A.2
  • 266
    • 84948986594 scopus 로고    scopus 로고
    • Effcient Deterministic Algorithms for Embedding Graphs on Books
    • [SS96] Jin-Yi Cai and Chak Kuen Wong, editors, Springer-Verlag, Lecture Notes in Computer Science
    • [SS96] Farhad Shahrokhi and Weiping Shi. Effcient Deterministic Algorithms for Embedding Graphs on Books. In Jin-Yi Cai and Chak Kuen Wong, editors, Proceedings 2nd Annual International Conference on Computing and Combinatorics, COCOON'96, pages 162-168. Springer-Verlag, Lecture Notes in Computer Science, vol. 1090, 1996.
    • (1996) Proceedings 2nd Annual International Conference on Computing and Combinatorics, COCOON'96 , vol.1090 , pp. 162-168
    • Shahrokhi, F.1    Shi, W.2
  • 270
    • 0347392615 scopus 로고    scopus 로고
    • Drawings of Graphs on Surfaces with Few Crossings
    • [SSSV96b]
    • [SSSV96b] Farhad Shahrokhi, László A. Székely, Ondrej Sýkora, and Imrich Vrt'o. Drawings of Graphs on Surfaces with Few Crossings. Algorithmica,16:118-131, 1996.
    • (1996) Algorithmica , vol.16 , pp. 118-131
    • Shahrokhi, F.1    Székely, L.A.2    Sýkora, O.3    Vrt'o, I.4
  • 271
    • 84947909366 scopus 로고    scopus 로고
    • On Bipartite Crossings, Largest Biplanar Subgraphs, and the Linear Arrangement Problem
    • [SSSV97] Frank Dehne, Andrew Rau-Chaplin, Jörg-Rüdiger Sack, and Roberto Tamassia, editors, Springer-Verlag, Lecture Notes in Computer Science
    • [SSSV97] Farhad Shahrokhi, Ondrej Sýkora, László A. Székely, and Imrich Vrt'o. On Bipartite Crossings, Largest Biplanar Subgraphs, and the Linear Arrangement Problem. In Frank Dehne, Andrew Rau-Chaplin, Jörg-Rüdiger Sack, and Roberto Tamassia, editors, Proceedings 5th International Workshop on Algorithms and Data Structures, WADS'97, Halifax, Nova Scotia, Canada, August 6-8, 1997, pages 55-68. Springer-Verlag, Lecture Notes in Computer Science, vol. 1272, 1997.
    • (1997) Proceedings 5th International Workshop on Algorithms and Data Structures, WADS'97, Halifax, Nova Scotia, Canada, August 6-8, 1997 , vol.1272 , pp. 55-68
    • Shahrokhi, F.1    Sýkora, O.2    Székely, L.A.3    Vrt'o, I.4
  • 273
    • 0347269333 scopus 로고    scopus 로고
    • A new lower bound for the bipartite crossing number with applications
    • [SSSV00]
    • [SSSV00] Farhad Shahrokhi, Ondrej Sýkora, László A. Székely, and Imrich Vrt'o. A new lower bound for the bipartite crossing number with applications. Theoretical Computer Science, 245:281-294, 2000.
    • (2000) Theoretical Computer Science , vol.245 , pp. 281-294
    • Shahrokhi, F.1    Sýkora, O.2    Székely, L.A.3    Vrt'o, I.4
  • 274
    • 84957605453 scopus 로고
    • Crossing Numbers of Graphs, Lower Bound Techniques and Algorithms: A Survey
    • [SSV95] Roberto Tamassia and Ioannis G. Tollis, editors, Springer-Verlag, Lecture Notes in Computer Science, vol.
    • [SSV95] Farhad Shahrokhi, László A. Székely, and Imrich Vrt'o. Crossing Numbers of Graphs, Lower Bound Techniques and Algorithms: A Survey. In Roberto Tamassia and Ioannis G. Tollis, editors, Graph Drawing. Proceedings of the DIMACS International Workshop, GD'94, pages 131-142. Springer-Verlag, Lecture Notes in Computer Science, vol. 894, 1995.
    • (1995) Graph Drawing. Proceedings of the DIMACS International Workshop, GD'94 , vol.894 , pp. 131-142
    • Shahrokhi, F.1    Székely, L.A.2    Vrt'o, I.3
  • 276
    • 0011614162 scopus 로고
    • On the crossing number of the hypercube and the cube connected cycles
    • [SV92] G. Schmidt and R. Berghammer, editors, Springer-Verlag, Lecture Notes in Computer Science
    • [SV92] Ondrej Sýkora and Imrich Vrt'o. On the crossing number of the hypercube and the cube connected cycles. In G. Schmidt and R. Berghammer, editors, Proceedings 17th International Workshop on Graph-Theoretic Concepts in Computer Science, WG'91, pages 214-218. Springer-Verlag, Lecture Notes in Computer Science, vol. 570, 1992.
    • (1992) Proceedings 17th International Workshop on Graph-Theoretic Concepts in Computer Science, WG'91 , vol.570 , pp. 214-218
    • Sýkora, O.1    Vrt'o, I.2
  • 277
    • 0027589605 scopus 로고
    • Edge separators for graphs of bounded genus with applications
    • [SV93a]
    • [SV93a] Ondrej Sýkora and Imrich Vrt'o. Edge separators for graphs of bounded genus with applications. Theoretical Computer Science, 112:419-429,1993.
    • (1993) Theoretical Computer Science , vol.112 , pp. 419-429
    • Sýkora, O.1    Vrt'o, I.2
  • 278
    • 1542711034 scopus 로고
    • On crossing numbers of hypercubes and cube connected cycles
    • [SV93b]
    • [SV93b] Ondrej Sýkora and Imrich Vrt'o. On crossing numbers of hypercubes and cube connected cycles. BIT, 33:232-237, 1993.
    • (1993) BIT , vol.33 , pp. 232-237
    • Sýkora, O.1    Vrt'o, I.2
  • 279
    • 0028481584 scopus 로고
    • On VLSI layout of the star graph and related networks
    • [SV94] Ondrej Sýkora and Imrich Vrt'o. On VLSI layout of the star graph and related networks. INTEGRATION The VLSI Journal, 17:83-93, 1994.
    • (1994) INTEGRATION the VLSI Journal , vol.17 , pp. 83-93
    • Sýkora, O.1    Vrt'o, I.2
  • 280
    • 38249026284 scopus 로고
    • The Graph Genus Problem Is NP-Complete
    • [Tho89]
    • [Tho89] Carsten Thomassen. The Graph Genus Problem Is NP-Complete. J. Algorithms, 10:568-576, 1989.
    • (1989) J. Algorithms , vol.10 , pp. 568-576
    • Thomassen, C.1
  • 282
    • 0037648004 scopus 로고
    • A near-optimum parallel planarization algorithm
    • [TL89]
    • [TL89] Yoshiyasu Takefuji and Kuo Chun Lee. A near-optimum parallel planarization algorithm. Science, 245:1221-1223, 1989.
    • (1989) Science , vol.245 , pp. 1221-1223
    • Takefuji, Y.1    Lee, K.C.2
  • 286
    • 21944439637 scopus 로고    scopus 로고
    • A Characterization of Planar Graphs by Pseudo-Line Arrangements
    • [TT97] Springer-Verlag, Lecture Notes in Computer Science
    • [TT97] Hisao Tamaki and Takeshi Tokuyama. A Characterization of Planar Graphs by Pseudo-Line Arrangements. In Algorithms and Computation, 8th International Symposium, ISAAC'97, pages 133-142. Springer-Verlag, Lecture Notes in Computer Science, vol. 1350, 1997.
    • (1997) Algorithms and Computation, 8th International Symposium, ISAAC'97 , vol.1350 , pp. 133-142
    • Tamaki, H.1    Tokuyama, T.2
  • 287
    • 0002604170 scopus 로고
    • A Note of Welcome
    • [Tur77]
    • [Tur77] Paul Turán. A Note of Welcome. J. of Graph Theory, 1:7-9, 1977.
    • (1977) J. of Graph Theory , vol.1 , pp. 7-9
    • Turán, P.1
  • 289
    • 0041770273 scopus 로고
    • The non-biplanar character of the complete 9-graph
    • [Tut63a]
    • [Tut63a] William T. Tutte. The non-biplanar character of the complete 9-graph. Canad. Math. Bull., 6:319-330, 1963.
    • (1963) Canad. Math. Bull. , vol.6 , pp. 319-330
    • Tutte, W.T.1
  • 293
    • 84957354737 scopus 로고    scopus 로고
    • Graph Drawing with no k Pairwise Crossing Edges
    • [Val97] Giuseppe Di Battista, editor, Springer-Verlag, Lecture Notes in Computer Science
    • [Val97] Pavel Valtr. Graph Drawing with no k Pairwise Crossing Edges. In Giuseppe Di Battista, editor, Proceedings of the Symposium on Graph Drawing, GD'97, pages 205-218. Springer-Verlag, Lecture Notes in Computer Science, vol. 1353, 1997.
    • (1997) Proceedings of the Symposium on Graph Drawing, GD'97 , vol.1353 , pp. 205-218
    • Valtr, P.1
  • 294
    • 0032391089 scopus 로고    scopus 로고
    • On Geometric Graphs with No k Pairwise Parallel Edges
    • [Val98]
    • [Val98] Pavel Valtr. On Geometric Graphs with No k Pairwise Parallel Edges. Discrete Comput. Geom., 19:461-469, 1998.
    • (1998) Discrete Comput. Geom. , vol.19 , pp. 461-469
    • Valtr, P.1
  • 297
    • 0001855349 scopus 로고
    • Bemerkungen zum Vierfarbenproblem
    • [Wag36]
    • [Wag36] K. Wagner. Bemerkungen zum Vierfarbenproblem. Jber. d. Dt. Math.-Verein., 46:26-32, 1936.
    • (1936) Jber. D. Dt. Math.-Verein. , vol.46 , pp. 26-32
    • Wagner, K.1
  • 298
    • 33845337775 scopus 로고
    • Über eine Eigenschaft der ebenen Komplexe
    • [Wag37a]
    • [Wag37a] K. Wagner. Über eine Eigenschaft der ebenen Komplexe. Math. Ann., 114:570-590, 1937.
    • (1937) Math. Ann. , vol.114 , pp. 570-590
    • Wagner, K.1
  • 299
    • 0009227317 scopus 로고
    • Über eine Erweiterung eines Satzes von Kuratowski
    • [Wag37b]
    • [Wag37b] K.Wagner. Über eine Erweiterung eines Satzes von Kuratowski. Deutsche Mathematik, 2:280-285, 1937.
    • (1937) Deutsche Mathematik , vol.2 , pp. 280-285
    • Wagner, K.1
  • 300
    • 0020750943 scopus 로고
    • On the NPhardness of edge-deletion and -contraction problems
    • [WAN83]
    • [WAN83] Toshimasa Watanabe, Tadashi Ae, and Akira Nakamura. On the NPhardness of edge-deletion and -contraction problems. Discrete Applied Math., 6:63-78, 1983.
    • (1983) Discrete Applied Math. , vol.6 , pp. 63-78
    • Watanabe, T.1    Ae, T.2    Nakamura, A.3
  • 301
    • 0002602647 scopus 로고
    • Topological Graph Theory
    • [WB78] Lowell W. Beineke and Robin J. Wilson, editors, Academic Press, New York
    • [WB78] Arthur T. White and Lowell W. Beineke. Topological Graph Theory. In Lowell W. Beineke and Robin J. Wilson, editors, Selected Topics in Graph Theory, pages 15-49. Academic Press, New York, 1978.
    • (1978) Selected Topics in Graph Theory , pp. 15-49
    • White, A.T.1    Beineke, L.W.2
  • 302
    • 0347419644 scopus 로고    scopus 로고
    • Edge-disjoint (s,t)-paths in undirected planar graphs in linear time
    • [Wei97]
    • [Wei97] Karsten Weihe. Edge-disjoint (s,t)-paths in undirected planar graphs in linear time. J. Algorithms, 23:121-138, 1997.
    • (1997) J. Algorithms , vol.23 , pp. 121-138
    • Weihe, K.1
  • 304
    • 84864592098 scopus 로고
    • Thickness-critical graphs - A generalization of Kuratowski's topic
    • [Wes83b] M. Borowiecki, J.W. Kennedy, and Maciej M. Sysło, editors, Springer-Verlag, Lecture Notes in Mathematics
    • [Wes83b] Walter Wessel. Thickness-critical graphs - a generalization of Kuratowski's topic. In M. Borowiecki, J.W. Kennedy, and Maciej M. Sysło, editors, Graph Theory, Proc. of a Conference held in Łagów, Poland, February 10-13, 1981, pages 266-277. Springer-Verlag, Lecture Notes in Mathematics, vol. 1018, 1983.
    • (1983) Graph Theory, Proc. of a Conference Held in Łagów, Poland, February 10-13, 1981 , vol.1018 , pp. 266-277
    • Wessel, W.1
  • 307
    • 77957091946 scopus 로고
    • Construction of Critical Graphs by Replacing Edges
    • [Wes89] Lars Døvling Andersen and Gabriel A. Dirac, editors, North-Holland, Annals of Discrete Mathematics
    • [Wes89] Walter Wessel. Construction of Critical Graphs by Replacing Edges. In Lars Døling Andersen and Gabriel A. Dirac, editors, Graph theory in memory of G. A. Dirac, pages 473-486. North-Holland, Annals of Discrete Mathematics, vol. 41, 1989.
    • (1989) Graph Theory in Memory of G. A. Dirac , vol.41 , pp. 473-486
    • Wessel, W.1
  • 310
    • 0342912646 scopus 로고
    • Planar graphs
    • [Whi33]
    • [Whi33] Hassler Whitney. Planar graphs. Fundamenta Mathematicae, 21:245-254,1933.
    • (1933) Fundamenta Mathematicae , vol.21 , pp. 245-254
    • Whitney, H.1
  • 312
    • 0010764232 scopus 로고
    • Embedding graphs in the plane - Algorithmic aspects
    • [Wil80] J. Srivastava, editor, North-Holland, Annals of Discrete Mathematics
    • [Wil80] S.G. Williamson. Embedding graphs in the plane - algorithmic aspects. In J. Srivastava, editor, Combinatorial Mathematics, Optimal Designs and their Applications, pages 349-384. North-Holland, Annals of Discrete Mathematics, vol. 6, 1980.
    • (1980) Combinatorial Mathematics, Optimal Designs and Their Applications , vol.6 , pp. 349-384
    • Williamson, S.G.1
  • 313
    • 84986462345 scopus 로고
    • An Eulerian Trail through Königsberg
    • [Wil86]
    • [Wil86] Robin J. Wilson. An Eulerian Trail through Königsberg. J. of Graph Theory, 10:265-275, 1986.
    • (1986) J. of Graph Theory , vol.10 , pp. 265-275
    • Wilson, R.J.1
  • 314
    • 84987505805 scopus 로고
    • Cyclic-Order Graphs and Zarankiewicz's Crossing-Number Conjecture
    • [Woo93]
    • [Woo93] D.R.Woodall. Cyclic-Order Graphs and Zarankiewicz's Crossing-Number Conjecture. J. of Graph Theory, 17:657-671, 1993.
    • (1993) J. of Graph Theory , vol.17 , pp. 657-671
    • Woodall, D.R.1
  • 316
    • 0000603383 scopus 로고
    • Edge-deletion problems
    • [Yan81]
    • [Yan81] Mihalis Yannakakis. Edge-deletion problems. SIAM J. Comput., 10:297-309, 1981.
    • (1981) SIAM J. Comput. , vol.10 , pp. 297-309
    • Yannakakis, M.1
  • 318
    • 0024605964 scopus 로고
    • Embedding Planar Graphs in Four Pages
    • [Yan89]
    • [Yan89] Mihalis Yannakakis. Embedding Planar Graphs in Four Pages. J. Computer and System Sciences, 38:36-67, 1989.
    • (1989) J. Computer and System Sciences , vol.38 , pp. 36-67
    • Yannakakis, M.1
  • 319
    • 84986447872 scopus 로고
    • A construction of chromatic index critical graphs
    • [Yap81]
    • [Yap81] Hian Poh Yap. A construction of chromatic index critical graphs. J. of Graph Theory, 5:159-163, 1981.
    • (1981) J. of Graph Theory , vol.5 , pp. 159-163
    • Yap, H.P.1
  • 320
    • 85039510602 scopus 로고
    • A class of chromatic index critical graphs
    • [Yap83]
    • [Yap83] Hian Poh Yap. A class of chromatic index critical graphs. Bull. Malays. Math. Soc.,II. Ser., 6:45-46, 1983.
    • (1983) Bull. Malays. Math. Soc.,II. Ser. , vol.6 , pp. 45-46
    • Yap, H.P.1
  • 321
    • 84957811100 scopus 로고    scopus 로고
    • An Approximation Algorithms for the Two-Layered Graph Drawing Problem
    • [YS99] Takao Asano, Hiroshi Imai, D.T. Lee, Shin-ichi Nakano, and Takeshi Tokuyama, editors, Springer-Verlag, Lecture Notes in Computer Science
    • [YS99] Atsuko Yamaguchi and Akihiro Sugimoto. An Approximation Algorithms for the Two-Layered Graph Drawing Problem. In Takao Asano, Hiroshi Imai, D.T. Lee, Shin-ichi Nakano, and Takeshi Tokuyama, editors, Proceedings 5th Annual International Conference on Computing and Combinatorics, COCOON'99, pages 81-91. Springer-Verlag, Lecture Notes in Computer Science, vol. 1627, 1999.
    • (1999) Proceedings 5th Annual International Conference on Computing and Combinatorics, COCOON'99 , vol.1627 , pp. 81-91
    • Yamaguchi, A.1    Sugimoto, A.2
  • 322
    • 0346131675 scopus 로고
    • On a problem of P. Turán concerning graphs
    • [Zar54]
    • [Zar54] K. Zarankiewicz. On a problem of P. Turán concerning graphs. Fundamenta Mathematicae, 41:137-145, 1954.
    • (1954) Fundamenta Mathematicae , vol.41 , pp. 137-145
    • Zarankiewicz, K.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.