메뉴 건너뛰기




Volumn 23, Issue 2, 2009, Pages 909-939

Clique-width is NP-complete

Author keywords

Absolute approximation; Clique width; NP completeness; Pathwidth

Indexed keywords

3-COLORABILITY; CLIQUE-WIDTH; GRAPH G; GRAPH PARAMETERS; GRAPH PROBLEMS; MONADIC SECOND-ORDER LOGIC; NP COMPLETE; NP-COMPLETENESS; NP-HARD PROBLEM; PATHWIDTH; POLYNOMIAL-TIME; SECOND ORDERS; VERTEX SET;

EID: 73349137261     PISSN: 08954801     EISSN: None     Source Type: Journal    
DOI: 10.1137/070687256     Document Type: Article
Times cited : (135)

References (35)
  • 2
    • 0008799320 scopus 로고
    • Approximating tree- width, pathwidth, frontsize, and shortest elimination tree, J
    • H. L. BODLAENDER, J. R. GILBERT, H. HAFSTEINSSON, AND T. KLOKS, Approximating tree- width, pathwidth, frontsize, and shortest elimination tree, J. Algorithms, 18 (1995), pp. 238-255.
    • (1995) Algorithms , vol.18 , pp. 238-255
    • BODLAENDER, H.L.1    GILBERT, J.R.2    HAFSTEINSSON, H.3    KLOKS, T.4
  • 3
    • 84878661172 scopus 로고    scopus 로고
    • On the clique-width of graphs in hereditary classes
    • Algorithms and Computation, Springer-Verlag, Berlin
    • R. BOLIAC AND V. LOZIN, On the clique-width of graphs in hereditary classes, in Algorithms and Computation, Lecture Notes in Comput. Sci. 2518, Springer-Verlag, Berlin, 2002, pp. 44-54.
    • (2002) Lecture Notes in Comput. Sci , vol.2518 , pp. 44-54
    • BOLIAC, R.1    LOZIN, V.2
  • 5
    • 33745046651 scopus 로고    scopus 로고
    • A. BRANDSTÄDT, J. ENGELFRIET, H.-O. LE, AND V. V. LOZIN, Clique-width for 4-vertex forbidden subgraphs, Theory Comput. Syst., 39 (2006), p p. 561-590.
    • A. BRANDSTÄDT, J. ENGELFRIET, H.-O. LE, AND V. V. LOZIN, Clique-width for 4-vertex forbidden subgraphs, Theory Comput. Syst., 39 (2006), p p. 561-590.
  • 6
    • 24344452559 scopus 로고    scopus 로고
    • On the relationship between clique-width and treewidth
    • D. G. CORNEIL AND U. ROTICS, On the relationship between clique-width and treewidth, SIAM J. Comput., 34 (2005), pp. 825-847.
    • (2005) SIAM J. Comput , vol.34 , pp. 825-847
    • CORNEIL, D.G.1    ROTICS, U.2
  • 7
    • 73349106025 scopus 로고    scopus 로고
    • An extended abstract appeared in the Proceedings of Graph-Theoretic Concepts in Computer Science WG 2001, Lecture Notes in Comput. Sci. 2204, Springer-Verlag, Berlin, 2001, pp. 78-90
    • An extended abstract appeared in the Proceedings of Graph-Theoretic Concepts in Computer Science (WG 2001), Lecture Notes in Comput. Sci. 2204, Springer-Verlag, Berlin, 2001, pp. 78-90.
  • 8
    • 84896754098 scopus 로고    scopus 로고
    • Polynomial time recognition of clique-width ≤ 3 graphs (extended abstract)
    • Symposium, G. H. Gonnet, D. Panario, and A. Viola, eds, Lecture Notes in Comput. Sci. 1776, Springer-Verlag, Berlin
    • D. G. CORNEIL, M. HABIB, J.-M. LANLIGNEL, B. A. REED, AND U. ROTICS, Polynomial time recognition of clique-width ≤ 3 graphs (extended abstract), in LATIN 2000: Theoretical Informatics, 4th Latin American Symposium, G. H. Gonnet, D. Panario, and A. Viola, eds., Lecture Notes in Comput. Sci. 1776, Springer-Verlag, Berlin, 2000, pp. 126-134.
    • (2000) LATIN 2000: Theoretical Informatics, 4th Latin American , pp. 126-134
    • CORNEIL, D.G.1    HABIB, M.2    LANLIGNEL, J.-M.3    REED, B.A.4    ROTICS, U.5
  • 9
    • 0000413488 scopus 로고
    • A logical characterization of the sets of hypergraphs defined by hyperedge replacement grammars
    • B. COURCELLE AND J. ENGELFRIET, A logical characterization of the sets of hypergraphs defined by hyperedge replacement grammars, Math. Systems Theory, 28 (1995), pp. 515-552.
    • (1995) Math. Systems Theory , vol.28 , pp. 515-552
    • COURCELLE, B.1    ENGELFRIET, J.2
  • 10
    • 0027553197 scopus 로고
    • Monadic second-order evaluations on tree-decomposable graphs
    • B. COURCELLE AND M. MOSBAH, Monadic second-order evaluations on tree-decomposable graphs, Theoret. Comput. Sci., 109 (1993), pp. 49-82.
    • (1993) Theoret. Comput. Sci , vol.109 , pp. 49-82
    • COURCELLE, B.1    MOSBAH, M.2
  • 11
    • 0002015577 scopus 로고    scopus 로고
    • Upper bounds to the clique-width of graphs
    • B. COURCELLE AND S. OLARIU, Upper bounds to the clique-width of graphs, Discrete Appl. Math., 101 (2000), pp. 77-114.
    • (2000) Discrete Appl. Math , vol.101 , pp. 77-114
    • COURCELLE, B.1    OLARIU, S.2
  • 12
    • 33751429952 scopus 로고    scopus 로고
    • Vertex-minors, monadic second-order logic and a conjecture by Seese
    • B. COURCELLE AND S. OUM, Vertex-minors, monadic second-order logic and a conjecture by Seese, J. Combin. Theory Ser. B, 97 (2007), pp. 91-126.
    • (2007) J. Combin. Theory Ser. B , vol.97 , pp. 91-126
    • COURCELLE, B.1    OUM, S.2
  • 13
    • 85013107592 scopus 로고
    • Context-free handle-rewriting hypergraph grammars
    • Proceedings of the Graph-Grammars and Their Application to Computer Science, 4th International Workshop Bremen, Germany, 1990, H. Ehrig, H.-J. Kreowski, and G. Rozenberg, eds, Springer-Verlag, Berlin
    • B. COURCELLE, J. ENGELFRIET, AND G. ROZENBERG, Context-free handle-rewriting hypergraph grammars, in Proceedings of the Graph-Grammars and Their Application to Computer Science, 4th International Workshop (Bremen, Germany, 1990), H. Ehrig, H.-J. Kreowski, and G. Rozenberg, eds., Lecture Notes in Comput. Sci. 532, Springer-Verlag, Berlin, 1991, pp. 253-268.
    • (1991) Lecture Notes in Comput. Sci , vol.532 , pp. 253-268
    • COURCELLE, B.1    ENGELFRIET, J.2    ROZENBERG, G.3
  • 15
    • 0034399867 scopus 로고    scopus 로고
    • Linear time solvable optimization problems on graphs of bounded clique-width
    • B. COURCELLE, J. A. MAKOWSKY, AND U. ROTICS, Linear time solvable optimization problems on graphs of bounded clique-width, Theory Comput. Syst., 33 (2000), pp. 125-150.
    • (2000) Theory Comput. Syst , vol.33 , pp. 125-150
    • COURCELLE, B.1    MAKOWSKY, J.A.2    ROTICS, U.3
  • 16
    • 0001780070 scopus 로고    scopus 로고
    • On the fixed parameter complexity of graph enumeration problems definable in monadic second-order logic
    • B. COURCELLE, J. A. MAKOWSKY, AND U. ROTICS, On the fixed parameter complexity of graph enumeration problems definable in monadic second-order logic, Discrete Appl. Math., 108 (2001), pp. 23-52.
    • (2001) Discrete Appl. Math , vol.108 , pp. 23-52
    • COURCELLE, B.1    MAKOWSKY, J.A.2    ROTICS, U.3
  • 17
    • 4043179684 scopus 로고    scopus 로고
    • Deciding clique-width for graphs of bounded tree-width
    • W. ESPELAGE, F. GURSKI, AND E. WANKE, Deciding clique-width for graphs of bounded tree-width, J. Graph Algorithms Appl., 7 (2003), pp. 141-180.
    • (2003) J. Graph Algorithms Appl , vol.7 , pp. 141-180
    • ESPELAGE, W.1    GURSKI, F.2    WANKE, E.3
  • 18
    • 73349137107 scopus 로고    scopus 로고
    • M. R. FELLOWS, F. A. ROSAMOND, U. ROTICS, AND S. SZEIDER, Proving NP-Hardness for Clique-Width I: Non-approximability of Sequential Clique-Width, Technical report TR05-080, Revision 01, Electronic Colloquium on Computational Complexity, HPI, Potsdam, Germany, 2005.
    • M. R. FELLOWS, F. A. ROSAMOND, U. ROTICS, AND S. SZEIDER, Proving NP-Hardness for Clique-Width I: Non-approximability of Sequential Clique-Width, Technical report TR05-080, Revision 01, Electronic Colloquium on Computational Complexity, HPI, Potsdam, Germany, 2005.
  • 19
    • 33748114756 scopus 로고    scopus 로고
    • Graph searching, elimination trees, and a generalization of bandwidth
    • Fundamentals of Computation Theory, Springer-Verlag, Berlin
    • F. V. FOMIN, P. HEGGERNES, AND J. A. TELLE, Graph searching, elimination trees, and a generalization of bandwidth, in Fundamentals of Computation Theory, Lecture Notes in Comput. Sci. 2751, Springer-Verlag, Berlin, 2003, pp. 73-85.
    • (2003) Lecture Notes in Comput. Sci , vol.2751 , pp. 73-85
    • FOMIN, F.V.1    HEGGERNES, P.2    TELLE, J.A.3
  • 20
    • 0345686491 scopus 로고    scopus 로고
    • NCE graph grammars and clique-width
    • Graph-Theoretic Concepts in Computer Science, Springer-Verlag, Berlin
    • A. GLIKSON AND J. A. MAKOWSKY, NCE graph grammars and clique-width, in Graph-Theoretic Concepts in Computer Science, Lecture Notes in Comput. Sci. 2880, Springer-Verlag, Berlin, 2003, pp. 237-248.
    • (2003) Lecture Notes in Comput. Sci , vol.2880 , pp. 237-248
    • GLIKSON, A.1    MAKOWSKY, J.A.2
  • 21
    • 32544456105 scopus 로고    scopus 로고
    • Minimizing NLC-width is NP-complete (extended abstract)
    • Graph-Theoretic Concepts in Computer Science, Springer-Verlag, Berlin
    • F. GURSKI AND E. WANKE, Minimizing NLC-width is NP-complete (extended abstract), in Graph-Theoretic Concepts in Computer Science, Lecture Notes in Comput. Sci. 3787, Springer-Verlag, Berlin, 2005, pp. 69-80.
    • (2005) Lecture Notes in Comput. Sci , vol.3787 , pp. 69-80
    • GURSKI, F.1    WANKE, E.2
  • 22
    • 27844491884 scopus 로고    scopus 로고
    • On the relationship between NLC-width and linear NLC-width
    • F. GURSKI AND E. WANKE, On the relationship between NLC-width and linear NLC-width, Theoret. Comput. Sci., 347 (2005), pp. 76-89.
    • (2005) Theoret. Comput. Sci , vol.347 , pp. 76-89
    • GURSKI, F.1    WANKE, E.2
  • 23
    • 33746356242 scopus 로고    scopus 로고
    • Vertex disjoint paths on clique-width bounded graphs
    • F. GURSKI AND E. WANKE, Vertex disjoint paths on clique-width bounded graphs, Theoret. Comput. Sci., 359 (2006), pp. 188-199.
    • (2006) Theoret. Comput. Sci , vol.359 , pp. 188-199
    • GURSKI, F.1    WANKE, E.2
  • 24
    • 4043101495 scopus 로고    scopus 로고
    • Clique-decomposition, NLC-decomposition, and modular decomposition - Relationships and results for random graphs
    • Ö. JOHANSSON, Clique-decomposition, NLC-decomposition, and modular decomposition - Relationships and results for random graphs, Congr. Numer., 132 (1998), pp. 39-60.
    • (1998) Congr. Numer , vol.132 , pp. 39-60
    • JOHANSSON, O.1
  • 25
    • 73349130897 scopus 로고    scopus 로고
    • M. KARPINSKI AND J. WIRTGEN, On Approximation Hardness of the Bandwidth Problem, Technical report TR97-041, ECCC, Electronic Colloquium on Computational Complexity, HPI, Potsdam, Germany, 1997.
    • M. KARPINSKI AND J. WIRTGEN, On Approximation Hardness of the Bandwidth Problem, Technical report TR97-041, ECCC, Electronic Colloquium on Computational Complexity, HPI, Potsdam, Germany, 1997.
  • 26
    • 0026897421 scopus 로고
    • The vertex separation number of a graph equals its path-width
    • N. G. KINNERSLEY, The vertex separation number of a graph equals its path-width, Inform. Process. Lett., 42 (1992), pp. 345-350.
    • (1992) Inform. Process. Lett , vol.42 , pp. 345-350
    • KINNERSLEY, N.G.1
  • 27
    • 84867942957 scopus 로고    scopus 로고
    • Edge dominating set and colorings on graphs with fixed clique- width
    • D. KOBLER AND U. ROTICS, Edge dominating set and colorings on graphs with fixed clique- width, Discrete Appl. Math., 126 (2003), pp. 197-221.
    • (2003) Discrete Appl. Math , vol.126 , pp. 197-221
    • KOBLER, D.1    ROTICS, U.2
  • 28
    • 2442659456 scopus 로고    scopus 로고
    • Chordal bipartite graphs of bounded tree- and clique-width
    • V. LOZIN AND D. RAUTENBACH, Chordal bipartite graphs of bounded tree- and clique-width, Discrete Math., 283 (2004), pp. 151-158.
    • (2004) Discrete Math , vol.283 , pp. 151-158
    • LOZIN, V.1    RAUTENBACH, D.2
  • 29
    • 14644433034 scopus 로고    scopus 로고
    • On the band-, tree-, and clique-width of graphs with bounded vertex degree
    • V. LOZIN AND D. RAUTENBACH, On the band-, tree-, and clique-width of graphs with bounded vertex degree, SIAM J. Discrete Math., 18 (2004), pp. 195-206.
    • (2004) SIAM J. Discrete Math , vol.18 , pp. 195-206
    • LOZIN, V.1    RAUTENBACH, D.2
  • 31
    • 57849167967 scopus 로고    scopus 로고
    • Approximating rank-width and clique-width quickly
    • S. OUM, Approximating rank-width and clique-width quickly, ACM Trans. Algorithms, 5 (2008), pp. 1-20.
    • (2008) ACM Trans. Algorithms , vol.5 , pp. 1-20
    • OUM, S.1
  • 32
    • 32544455938 scopus 로고    scopus 로고
    • Approximating clique-width and branch-width
    • S. OUM AND P. SEYMOUR, Approximating clique-width and branch-width, J. Combin. Theory Ser. B, 96 (2006), pp. 514-528.
    • (2006) J. Combin. Theory Ser. B , vol.96 , pp. 514-528
    • OUM, S.1    SEYMOUR, P.2
  • 33
    • 0001221225 scopus 로고
    • The structure of the models of decidable mon adic theories of graphs
    • D. SEESE, The structure of the models of decidable mon adic theories of graphs, Ann. Pure Appl. Logic, 53 (1991), pp. 169-195.
    • (1991) Ann. Pure Appl. Logic , vol.53 , pp. 169-195
    • SEESE, D.1
  • 34
    • 0348046441 scopus 로고    scopus 로고
    • Clique-width of partner-limited graphs
    • J.-M. VANHERPE, Clique-width of partner-limited graphs, Discrete Math., 276 (2004), pp. 363-374.
    • (2004) Discrete Math , vol.276 , pp. 363-374
    • VANHERPE, J.-M.1
  • 35
    • 0039301943 scopus 로고
    • κ-NLC graphs and polynomial algorithms
    • E. WANKE, κ-NLC graphs and polynomial algorithms, Discrete Appl. Math., 54 (1994), pp. 251-266.
    • (1994) Discrete Appl. Math , vol.54 , pp. 251-266
    • WANKE, E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.