메뉴 건너뛰기




Volumn 14, Issue 1, 1998, Pages 59-73

The thickness of graphs: A survey

Author keywords

Branch and cut; Maximum planar subgraph; Thickness

Indexed keywords


EID: 0001833555     PISSN: 09110119     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00007219     Document Type: Article
Times cited : (103)

References (50)
  • 1
    • 38249034532 scopus 로고
    • On the genus and thickness of graphs
    • Asano, K.: On the genus and thickness of graphs, J. Comb. Theory Ser. B 43, 287-292 (1987)
    • (1987) J. Comb. Theory Ser. B , vol.43 , pp. 287-292
    • Asano, K.1
  • 2
    • 4043167917 scopus 로고
    • The thickness of an arbitrary complete graph
    • Alekseev, V.B., Gončakov, V.S.: The thickness of an arbitrary complete graph. Math. Sbornik 30(2), 187-202 (1976)
    • (1976) Math. Sbornik , vol.30 , Issue.2 , pp. 187-202
    • Alekseev, V.B.1    Gončakov, V.S.2
  • 3
    • 0026082425 scopus 로고
    • Multilayer grid embeddings for VLSI
    • Aggarwal, A., Klawe, M., Shor, P.: Multilayer grid embeddings for VLSI. Algorithmica 1, 129-151 (1991)
    • (1991) Algorithmica , vol.1 , pp. 129-151
    • Aggarwal, A.1    Klawe, M.2    Shor, P.3
  • 4
    • 4043172159 scopus 로고
    • Note on t-minimal bipartite graphs
    • Bouwer, I.Z., Broere, I.: Note on t-minimal 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
  • 5
    • 4043176433 scopus 로고
    • Complete bipartite graphs: Decomposition into planar subgraphs
    • F. Harary: New York
    • Beineke, L.W.: Complete bipartite graphs: Decomposition into planar subgraphs. In: F. Harary: A seminar on graph theory, pp. 42-53. New York: 1967.
    • (1967) A Seminar on Graph Theory , pp. 42-53
    • Beineke, L.W.1
  • 6
    • 0040200590 scopus 로고
    • The decomposition of complete graphs into planar subgraphs
    • New York: Academic Press
    • Beineke, L.W.: The decomposition of complete graphs into planar subgraphs. In: Graph theory and theoretical physics, pp. 139-153. New York: Academic Press, 1967
    • (1967) Graph Theory and Theoretical Physics , pp. 139-153
    • Beineke, L.W.1
  • 7
    • 0041642539 scopus 로고
    • Minimal decompositions of complete graphs into subgraphs with embeddability properties
    • Beineke, L.W.: Minimal decompositions of complete graphs into subgraphs with embeddability properties. Canad. J. Math. 21, 992-1000 (1969)
    • (1969) Canad. J. Math. , vol.21 , pp. 992-1000
    • Beineke, L.W.1
  • 9
    • 0040794967 scopus 로고
    • The thickness of the complete graph
    • Beineke, L. W., Harary, F.: The thickness of the complete graph. Canad. J. Math. 17, 850-859 (1965)
    • (1965) Canad. J. Math. , vol.17 , pp. 850-859
    • Beineke, L.W.1    Harary, F.2
  • 10
    • 84966248492 scopus 로고
    • Every planar graph with nine points has a nonplanar complement
    • Battle, J., Harary, F., Kodoma, Y.: Every planar graph with nine points has a nonplanar complement. Bull. Amer. Math Soc. 68, 569-571 (1962)
    • (1962) Bull. Amer. Math Soc. , vol.68 , pp. 569-571
    • Battle, J.1    Harary, F.2    Kodoma, Y.3
  • 12
    • 0026835958 scopus 로고
    • Embedding graphs in books: A survey
    • March
    • Bilski, T.: Embedding graphs in books: a survey. IEEE Proceedings-E, Vol. 139, No. 2, March 1992.
    • (1992) IEEE Proceedings-E , vol.139 , Issue.2
    • Bilski, T.1
  • 13
    • 0017216776 scopus 로고
    • Testing for the consecutive ones property, Interval graphs and graph planarity testing using PQ-tree algorithms
    • Booth, K.S., Lueker, G.S.: Testing for the consecutive ones property, Interval graphs and graph planarity testing using PQ-tree algorithms. J. of Computer and Systems Sciences 13, 335-379 (1976)
    • (1976) J. of Computer and Systems Sciences , vol.13 , pp. 335-379
    • Booth, K.S.1    Lueker, G.S.2
  • 14
  • 17
    • 0027829965 scopus 로고
    • An O(m log n)-Time algorithm for the maximal planar subgraph problem
    • Cai, J., Han, X., Tarjan, R.E.: An O(m log 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, J.1    Han, X.2    Tarjan, R.E.3
  • 20
    • 84957598804 scopus 로고
    • Rectangle-visibility representations of bipartite graphs
    • Extended Abstract, R. Tamassia and I. Tollis: Graph Drawing, Berlin Heidelberg New York: Springer
    • Dean, A.M., Hutchinson, J.P.: Rectangle-visibility representations of bipartite graphs, Extended Abstract, Lecture Notes in Computer Science 894: R. Tamassia and I. Tollis: Graph Drawing, pp. 159-166. Berlin Heidelberg New York: Springer 1995
    • (1995) Lecture Notes in Computer Science 894 , pp. 159-166
    • Dean, A.M.1    Hutchinson, J.P.2
  • 22
    • 18144408895 scopus 로고
    • Outerthickness and outercoarseness of graphs
    • Combinatorics, London: Cambridge University Press
    • Guy, R.K.: Outerthickness and outercoarseness of graphs, in: Combinatorics, London Math. Soc. Lecture Notes 13, pp. 57-60. London: Cambridge University Press 1974
    • (1974) London Math. Soc. Lecture Notes 13 , pp. 57-60
    • Guy, R.K.1
  • 23
    • 0026147819 scopus 로고
    • On the thickness of graphs of given degree
    • Halton, J.: On the thickness of graphs of given degree. Info. Sci. 54, 219-238 (1991)
    • (1991) Info. Sci. , vol.54 , pp. 219-238
    • Halton, J.1
  • 27
    • 84947928171 scopus 로고    scopus 로고
    • On Representations of some thickness-two graphs
    • Extended Abstract, F. Brandenburg: Graph Drawing '95 Berlin Heidelberg New York: Springer
    • Hutchinson, J., T. Shermer, Vince, A.: On Representations of some thickness-two graphs, Extended Abstract, Lecture Notes in Computer Science 1027, F. Brandenburg: Graph Drawing '95. pp. 324-332. Berlin Heidelberg New York: Springer 1996
    • (1996) Lecture Notes in Computer Science 1027 , pp. 324-332
    • Hutchinson, J.1    Shermer, T.2    Vince, A.3
  • 28
    • 0016117886 scopus 로고
    • Efficient planarity testing
    • Hopcroft, J., Tarjan, R.E.: Efficient planarity testing. J. ACM 21, 549-568 (1974)
    • (1974) J. ACM , vol.21 , pp. 549-568
    • Hopcroft, J.1    Tarjan, R.E.2
  • 29
    • 0010651208 scopus 로고
    • Solving the maximum planar subgraph problem by branch and cut
    • Jünger, M., Mutzel, P.: Solving the maximum planar subgraph problem by branch and cut. Proc. 3rd IPCO Conf. Erice, 1993
    • (1993) Proc. 3rd IPCO Conf. Erice
    • Jünger, M.1    Mutzel, P.2
  • 30
    • 0002066416 scopus 로고    scopus 로고
    • Maximum planar subgraph and nice embeddings: Practical layout tools
    • Jünger, M., Mutzel, P.: Maximum planar subgraph and nice embeddings: Practical layout tools, Algorithmica 16, No. 1 33-59 (1996)
    • (1996) Algorithmica , vol.16 , Issue.1 , pp. 33-59
    • Jünger, M.1    Mutzel, P.2
  • 32
    • 85034184858 scopus 로고    scopus 로고
    • personal communication
    • Jordan, E.: personal communication
    • Jordan, E.1
  • 35
    • 4043054553 scopus 로고
    • Die Dicke des n-dimensionalen Würfel-Graphen
    • Kleinert, M.: Die Dicke des n-dimensionalen Würfel-Graphen. J. Comb. Theory 3, 10-15 (1967)
    • (1967) J. Comb. Theory , vol.3 , pp. 10-15
    • Kleinert, M.1
  • 36
    • 4043172160 scopus 로고
    • The Problem of Computing a Maximal Planar Subgraph Using PQ-Trees is still not solved
    • ECMI'94, Kaiserslautern
    • Leipert, S.: The Problem of Computing a Maximal Planar Subgraph Using PQ-Trees is still not solved. Special proceedings for students pp. 95-110. ECMI'94, Kaiserslautern 1994
    • (1994) Special Proceedings for Students , pp. 95-110
    • Leipert, S.1
  • 38
    • 84975969582 scopus 로고
    • Determining the thickness of graphs is NP-hard
    • Mansfield, A.: Determining the thickness of graphs is NP-hard. Math. Proc. Cambridge Philos. Soc. 9, 9-23 (1983)
    • (1983) Math. Proc. Cambridge Philos. Soc. , vol.9 , pp. 9-23
    • Mansfield, A.1
  • 39
    • 0344526777 scopus 로고
    • 16 en Trois Graphes Planaires
    • 16 en Trois Graphes Planaires, J. Comb. Theory Ser. B 13, 71 (1972)
    • (1972) J. Comb. Theory Ser. B , vol.13 , pp. 71
    • Mayer, J.1
  • 40
    • 84881100274 scopus 로고
    • Edge-disjoint spanning trees of finite graphs
    • Nash-Williams, C.St.J.A.: Edge-disjoint spanning trees of finite graphs. J. London Math. Soc. 36, 445-450 (1961)
    • (1961) J. London Math. Soc. , vol.36 , pp. 445-450
    • Nash-Williams, C.St.J.A.1
  • 42
    • 0042143483 scopus 로고
    • Die torodiale Dicke des vollständigen Graphen
    • Ringel, G.: Die torodiale Dicke des vollständigen Graphen. Math. Z. 87, 19-26 (1965)
    • (1965) Math. Z. , vol.87 , pp. 19-26
    • Ringel, G.1
  • 45
    • 4043143719 scopus 로고
    • A construction of thickness-minimal graphs
    • Širáň, J., Horák, P.: A construction of thickness-minimal graphs. Discr. Math. 64, 262-268 (1987)
    • (1987) Discr. Math. , vol.64 , pp. 262-268
    • Širáň, J.1    Horák, P.2
  • 46
    • 0041770273 scopus 로고
    • The non-biplanar character of the complete 9-graph
    • Tutte, W.T.: 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
  • 47
    • 0013509835 scopus 로고
    • The thickness of a graph
    • Tutte, W.T.: The thickness of a graph. Indag. Math. 25, 567-577 (1963)
    • (1963) Indag. Math. , vol.25 , pp. 567-577
    • Tutte, W.T.1
  • 48
    • 85010512956 scopus 로고
    • Über die Zerlegung des vollständigen Graphen in paare planare Graphen
    • H. Sachs: Leipzig: Teubner
    • Walther, H.: Über die Zerlegung des vollständigen Graphen in paare planare Graphen. In: H. Sachs: Beiträge zur Graphentheorie, pp. 189-205. Leipzig: Teubner 1968
    • (1968) Beiträge zur Graphentheorie , pp. 189-205
    • Walther, H.1
  • 49
    • 85039487178 scopus 로고
    • On some variations of the thickness of a graph connected with colouring
    • Wessel, W.: On some variations of the thickness of a graph connected with colouring. In: Graphs and other combinatorial topics, Teubner Texte Math. 59 pp. 344-348, 1983
    • (1983) Graphs and Other Combinatorial Topics, Teubner Texte Math. , vol.59 , pp. 344-348
    • Wessel, W.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.