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Volumn 146, Issue 3, 2005, Pages 193-218

Recognition and computation of minimal triangulations for AT-free claw-free and co-comparability graphs

Author keywords

AT free claw free graphs; Bandwidth; Co comparability graphs; Interval graphs; Minimal triangulations; Partition refinement; Proper interval graphs

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; BANDWIDTH; COMPUTATIONAL METHODS; SET THEORY; TRIANGULATION;

EID: 12344338405     PISSN: 0166218X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.dam.2004.10.001     Document Type: Article
Times cited : (32)

References (51)
  • 2
    • 84901438169 scopus 로고    scopus 로고
    • Maximum cardinality search for computing minimal triangulations
    • Proceedings of the 28th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2002
    • A. Berry, J.R.S. Blair, P. Heggernes, Maximum cardinality search for computing minimal triangulations, Proceedings of the 28th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2002, Lecture Notes in Computer Science, vol. 2573, 2002, pp. 1-12.
    • (2002) Lecture Notes in Computer Science , vol.2573 , pp. 1-12
    • Berry, A.1    Blair, J.R.S.2    Heggernes, P.3
  • 3
    • 0041858125 scopus 로고    scopus 로고
    • Separability generalizes Dirac's theorem
    • A. Berry, and J.-P. Bordat Separability generalizes Dirac's theorem Discrete Appl. Math. 84 1998 43 53
    • (1998) Discrete Appl. Math. , vol.84 , pp. 43-53
    • Berry, A.1    Bordat, J.-P.2
  • 4
    • 0034911146 scopus 로고    scopus 로고
    • A practical algorithm for making filled graphs minimal
    • J.R.S. Blair, P. Heggernes, and J.A. Telle A practical algorithm for making filled graphs minimal Theoret. Comput. Sci. 250 2001 125 141
    • (2001) Theoret. Comput. Sci. , vol.250 , pp. 125-141
    • Blair, J.R.S.1    Heggernes, P.2    Telle, J.A.3
  • 5
    • 0017216776 scopus 로고
    • Testing for the consecutive ones property, internal graphs, and graph planarity using PQ-tree algorithms
    • K.S. Booth, and G.S. Lueker Testing for the consecutive ones property, internal graphs, and graph planarity using PQ-tree algorithms J. Comput. System Sci. 13 1976 335 379
    • (1976) J. Comput. System Sci. , vol.13 , pp. 335-379
    • Booth, K.S.1    Lueker, G.S.2
  • 7
    • 0344823719 scopus 로고    scopus 로고
    • A simple linear time LexBFS cograph recognition algorithm
    • Proceedings of the 29th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2003
    • A. Bretscher, D.G. Corneil, M. Habib, Chr. Paul, A simple linear time LexBFS cograph recognition algorithm, Proceedings of the 29th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2003, Lecture Notes in Computer Science, vol. 2880, 2003, pp. 119-130.
    • (2003) Lecture Notes in Computer Science , vol.2880 , pp. 119-130
    • Bretscher, A.1    Corneil, D.G.2    Habib, M.3    Paul, Chr.4
  • 8
    • 1642601796 scopus 로고    scopus 로고
    • A simple 3-sweep LBFS algorithm for the recognition of unit interval graphs
    • D.G. Corneil A simple 3-sweep LBFS algorithm for the recognition of unit interval graphs Discrete Appl. Math. 138 2004 371 379
    • (2004) Discrete Appl. Math. , vol.138 , pp. 371-379
    • Corneil, D.G.1
  • 12
    • 0032690142 scopus 로고    scopus 로고
    • Linear time algorithms for dominating pairs in asteroidal triple-free graphs
    • D.G. Corneil, St. Olariu, and L. Stewart Linear time algorithms for dominating pairs in asteroidal triple-free graphs SIAM J. Comput. 28 4 1999 1284 1297
    • (1999) SIAM J. Comput. , vol.28 , Issue.4 , pp. 1284-1297
    • Corneil, D.G.1    Olariu, St.2    Stewart, L.3
  • 13
    • 84949681561 scopus 로고    scopus 로고
    • Minimal elimination ordering inside a given chordal graph
    • Proceedings of the 23rd International Workshop on Graph-Theoretic Concepts in Computer Science, WG'97
    • E. Dahlhaus, Minimal elimination ordering inside a given chordal graph, Proceedings of the 23rd International Workshop on Graph-Theoretic Concepts in Computer Science, WG'97, Lecture Notes in Computer Science, vol. 1335, 1997, pp. 132-143.
    • (1997) Lecture Notes in Computer Science , vol.1335 , pp. 132-143
    • Dahlhaus, E.1
  • 14
    • 22044452103 scopus 로고    scopus 로고
    • Minimal elimination of planar graphs
    • Proceedings of SWAT 1998
    • E. Dahlhaus, Minimal elimination of planar graphs, Proceedings of SWAT 1998, Lecture Notes in Computer Science, vol. 1432, 1998, pp. 210-221.
    • (1998) Lecture Notes in Computer Science , vol.1432 , pp. 210-221
    • Dahlhaus, E.1
  • 15
    • 84867931650 scopus 로고    scopus 로고
    • Minimal elimination ordering for graphs of bounded degree
    • E. Dahlhaus Minimal elimination ordering for graphs of bounded degree Discrete Appl. Math. 116 2002 127 143
    • (2002) Discrete Appl. Math. , vol.116 , pp. 127-143
    • Dahlhaus, E.1
  • 16
    • 0030128324 scopus 로고    scopus 로고
    • Linear-time representation algorithm for proper circular-arc graphs and proper interval graphs
    • X. Deng, P. Hell, and J. Huang Linear-time representation algorithm for proper circular-arc graphs and proper interval graphs SIAM J. Comput. 25 1996 390 403
    • (1996) SIAM J. Comput. , vol.25 , pp. 390-403
    • Deng, X.1    Hell, P.2    Huang, J.3
  • 18
    • 12344257559 scopus 로고    scopus 로고
    • Interval degree and bandwidth of a graph
    • F.V. Fomin, and P.A. Golovach Interval degree and bandwidth of a graph Discrete Appl. Math. 129 2-3 2003 345 359
    • (2003) Discrete Appl. Math. , vol.129 , Issue.23 , pp. 345-359
    • Fomin, F.V.1    Golovach, P.A.2
  • 19
    • 84972514233 scopus 로고
    • Incidence matrices and interval graphs
    • D.R. Fulkerson, and O.A. Gross Incidence matrices and interval graphs Pacific J. Math. 15 1965 835 855
    • (1965) Pacific J. Math. , vol.15 , pp. 835-855
    • Fulkerson, D.R.1    Gross, O.A.2
  • 24
    • 0002482188 scopus 로고    scopus 로고
    • Lex-BFS and partition refinement, with applications to transitive orientation, interval graph recognition and consecutive ones testing
    • M. Habib, R. McConnell, Chr. Paul, and L. Viennot Lex-BFS and partition refinement, with applications to transitive orientation, interval graph recognition and consecutive ones testing Theoret. Comput. Sci. 234 2000 59 84
    • (2000) Theoret. Comput. Sci. , vol.234 , pp. 59-84
    • Habib, M.1    McConnell, R.2    Paul, Chr.3    Viennot, L.4
  • 25
    • 84867943153 scopus 로고    scopus 로고
    • On claw-free asteroidal triple-free graphs
    • H. Hempel, and D. Kratsch On claw-free asteroidal triple-free graphs Discrete Appl. Math. 121 2002 155 180
    • (2002) Discrete Appl. Math. , vol.121 , pp. 155-180
    • Hempel, H.1    Kratsch, D.2
  • 27
    • 3342950895 scopus 로고    scopus 로고
    • Fully dynamic algorithms for chordal graphs and split graphs
    • University of Victoria
    • L. Ibarra, Fully dynamic algorithms for chordal graphs and split graphs, Technical Report, University of Victoria, 2000.
    • (2000) Technical Report
    • Ibarra, L.1
  • 28
    • 0037668746 scopus 로고    scopus 로고
    • Pathwide, bandwidth, and completion problems to proper interval graphs with small cliques
    • H. Kaplan, and R. Shamir Pathwide, bandwidth, and completion problems to proper interval graphs with small cliques SIAM J. Comput. 25 3 1996 540 561
    • (1996) SIAM J. Comput. , vol.25 , Issue.3 , pp. 540-561
    • Kaplan, H.1    Shamir, R.2
  • 29
    • 84947735120 scopus 로고
    • Approximating the bandwidth for asteroidal triple-free graphs
    • Proceedings of the Third Annual European Symposium on Algorithms, ESA'95
    • T. Kloks, D. Kratsch, H. Müller, Approximating the bandwidth for asteroidal triple-free graphs, Proceedings of the Third Annual European Symposium on Algorithms, ESA'95, Lecture Notes in Computer Science, vol. 979, 1995, pp. 434-447.
    • (1995) Lecture Notes in Computer Science , vol.979 , pp. 434-447
    • Kloks, T.1    Kratsch, D.2    Müller, H.3
  • 30
    • 0011423220 scopus 로고    scopus 로고
    • Approximating the bandwidth for AT-free graphs
    • T. Kloks, D. Kratsch, and H. Müller Approximating the bandwidth for AT-free graphs J. Algorithms 32 1999 41 57
    • (1999) J. Algorithms , vol.32 , pp. 41-57
    • Kloks, T.1    Kratsch, D.2    Müller, H.3
  • 31
    • 0024610616 scopus 로고
    • An incremental linear-time algorithm for recognizing interval graphs
    • N. Korte, and R.H. Möhring An incremental linear-time algorithm for recognizing interval graphs SIAM J. Comput. 18 1 1989 68 81
    • (1989) SIAM J. Comput. , vol.18 , Issue.1 , pp. 68-81
    • Korte, N.1    Möhring, R.H.2
  • 33
    • 0000148891 scopus 로고
    • Domination on cocomparability graphs
    • D. Kratsch, and L. Stewart Domination on cocomparability graphs SIAM J. Discrete Math. 6 3 1993 400 417
    • (1993) SIAM J. Discrete Math. , vol.6 , Issue.3 , pp. 400-417
    • Kratsch, D.1    Stewart, L.2
  • 34
    • 0002215434 scopus 로고
    • Representation of finite graphs by a set of intervals on the real line
    • C.G. Lekkerkerker, and J.Ch. Boland Representation of finite graphs by a set of intervals on the real line Fundam. Math. 51 1962 45 64
    • (1962) Fundam. Math. , vol.51 , pp. 45-64
    • Lekkerkerker, C.G.1    Boland, J.Ch.2
  • 35
    • 38249002493 scopus 로고
    • Optimal greedy algorithms for indifference graphs
    • P.J. Looges, and St. Olariu Optimal greedy algorithms for indifference graphs Comput. Math. Appl. 25 1993 15 25
    • (1993) Comput. Math. Appl. , vol.25 , pp. 15-25
    • Looges, P.J.1    Olariu, St.2
  • 36
    • 0000848263 scopus 로고    scopus 로고
    • Modular decomposition and transitive orientation
    • R.M. McConnell, and J.P. Spinrad Modular decomposition and transitive orientation Discrete Math. 201 1-3 1999 180 241
    • (1999) Discrete Math. , vol.201 , Issue.13 , pp. 180-241
    • McConnell, R.M.1    Spinrad, J.P.2
  • 38
    • 1642642513 scopus 로고    scopus 로고
    • Recognizing and computing minimal triangulations efficiently
    • Institut für Informatik, Bayerische Julius-Maximilians-Universität Würzburg
    • D. Meister, Recognizing and computing minimal triangulations efficiently, Technical Report 302, Institut für Informatik, Bayerische Julius-Maximilians-Universität Würzburg, 2002.
    • (2002) Technical Report , vol.302
    • Meister, D.1
  • 39
    • 0037761694 scopus 로고    scopus 로고
    • Triangulating graphs without asteroidal triples
    • R.H. Möhring Triangulating graphs without asteroidal triples Discrete Appl. Math. 64 1996 281 287
    • (1996) Discrete Appl. Math. , vol.64 , pp. 281-287
    • Möhring, R.H.1
  • 40
    • 0025791186 scopus 로고
    • An optimal greedy heuristic to color interval graphs
    • St. Olariu An optimal greedy heuristic to color interval graphs Inform. Process. Lett. 37 1991 21 25
    • (1991) Inform. Process. Lett. , vol.37 , pp. 21-25
    • Olariu, St.1
  • 41
    • 0023566630 scopus 로고
    • Three partition refinement algorithms
    • R. Paige, and R.E. Tarjan Three partition refinement algorithms SIAM J. Comput. 16 6 1987 973 989
    • (1987) SIAM J. Comput. , vol.16 , Issue.6 , pp. 973-989
    • Paige, R.1    Tarjan, R.E.2
  • 42
    • 0037671519 scopus 로고    scopus 로고
    • A linear time recognition algorithm for proper interval graphs
    • B.S. Panda, and S.K. Das A linear time recognition algorithm for proper interval graphs Inform. Process. Lett. 87 2003 153 161
    • (2003) Inform. Process. Lett. , vol.87 , pp. 153-161
    • Panda, B.S.1    Das, S.K.2
  • 43
    • 0016881473 scopus 로고
    • The NP-completeness of the bandwidth minimization problem
    • Ch.H. Papadimitriou The NP-completeness of the bandwidth minimization problem Computing 16 1976 263 270
    • (1976) Computing , vol.16 , pp. 263-270
    • Papadimitriou, Ch.H.1
  • 45
    • 0000865792 scopus 로고    scopus 로고
    • Characterizations and algorithmic applications of chordal graph embeddings
    • A. Parra, and P. Scheffler Characterizations and algorithmic applications of chordal graph embeddings Discrete Appl. Math. 79 1997 171 188
    • (1997) Discrete Appl. Math. , vol.79 , pp. 171-188
    • Parra, A.1    Scheffler, P.2
  • 46
    • 0002930970 scopus 로고
    • Indifference graphs
    • F. Harary Academic Press New York
    • F.S. Roberts Indifference graphs F. Harary Proof Techniques in Graph Theory 1969 Academic Press New York 139 146
    • (1969) Proof Techniques in Graph Theory , pp. 139-146
    • Roberts, F.S.1
  • 47
    • 0014928358 scopus 로고
    • Triangulated graphs and the elimination process
    • D.J. Rose Triangulated graphs and the elimination process J. Math. Anal. Appl. 32 1970 597 609
    • (1970) J. Math. Anal. Appl. , vol.32 , pp. 597-609
    • Rose, D.J.1
  • 48
    • 0001580189 scopus 로고
    • Algorithmic aspects of vertex elimination on graphs
    • D.J. Rose, R.E. Tarjan, and G.S. Lueker Algorithmic aspects of vertex elimination on graphs SIAM J. Comput. 5 1976 266 283
    • (1976) SIAM J. Comput. , vol.5 , pp. 266-283
    • Rose, D.J.1    Tarjan, R.E.2    Lueker, G.S.3
  • 49
    • 0011464935 scopus 로고
    • An script O sign(n log n) algorithm for bandwidth of interval graphs
    • A.P. Sprague An script O sign(n log n) algorithm for bandwidth of interval graphs SIAM J. Discrete Math. 7 2 1994 213 220
    • (1994) SIAM J. Discrete Math. , vol.7 , Issue.2 , pp. 213-220
    • Sprague, A.P.1
  • 50
    • 0031274275 scopus 로고    scopus 로고
    • Software reliability via run-time result-checking
    • H. Wasserman, and M. Blum Software reliability via run-time result-checking J. ACM 44 6 1997 826 849
    • (1997) J. ACM , vol.44 , Issue.6 , pp. 826-849
    • Wasserman, H.1    Blum, M.2


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