메뉴 건너뛰기




Volumn 97, Issue 1, 2007, Pages 91-126

Vertex-minors, monadic second-order logic, and a conjecture by Seese

Author keywords

Clique width; Isotropic system; Local complementation; Monadic second order logic; Rank width; Seese's conjecture; Vertex minor

Indexed keywords


EID: 33751429952     PISSN: 00958956     EISSN: 10960902     Source Type: Journal    
DOI: 10.1016/j.jctb.2006.04.003     Document Type: Article
Times cited : (107)

References (52)
  • 2
    • 0040543016 scopus 로고
    • Isotropic systems
    • Bouchet A. Isotropic systems. European J. Combin. 8 3 (1987) 231-244
    • (1987) European J. Combin. , vol.8 , Issue.3 , pp. 231-244
    • Bouchet, A.1
  • 3
    • 38249028150 scopus 로고
    • Graphic presentations of isotropic systems
    • Bouchet A. Graphic presentations of isotropic systems. J. Combin. Theory Ser. B 45 1 (1988) 58-76
    • (1988) J. Combin. Theory Ser. B , vol.45 , Issue.1 , pp. 58-76
    • Bouchet, A.1
  • 4
    • 84986440371 scopus 로고
    • Transforming trees by successive local complementations
    • Bouchet A. Transforming trees by successive local complementations. J. Graph Theory 12 2 (1988) 195-207
    • (1988) J. Graph Theory , vol.12 , Issue.2 , pp. 195-207
    • Bouchet, A.1
  • 5
    • 0242344249 scopus 로고
    • κ-Transformations, local complementations and switching
    • Cycles and Rays. Montreal, PQ, 1987, Kluwer Acad. Publ., Dordrecht
    • Bouchet A. κ-Transformations, local complementations and switching. Cycles and Rays. Montreal, PQ, 1987. NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. vol. 301 (1990), Kluwer Acad. Publ., Dordrecht 41-50
    • (1990) NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. , vol.301 , pp. 41-50
    • Bouchet, A.1
  • 6
    • 38149145200 scopus 로고
    • Circle graph obstructions
    • Bouchet A. Circle graph obstructions. J. Combin. Theory Ser. B 60 1 (1994) 107-144
    • (1994) J. Combin. Theory Ser. B , vol.60 , Issue.1 , pp. 107-144
    • Bouchet, A.1
  • 8
    • 84896754098 scopus 로고    scopus 로고
    • Polynomial time recognition of clique-width ≤3 graphs (extended abstract)
    • LATIN 2000: Theoretical Informatics. 4th Latin American Symposium, Punta del Este, Uruguay, April 10-14, 2000. Gonnet G.H., et al. (Ed), Springer, Berlin
    • Corneil D.G., Habib M., Lanlignel J.-M., Reed B., and Rotics U. Polynomial time recognition of clique-width ≤3 graphs (extended abstract). In: Gonnet G.H., et al. (Ed). LATIN 2000: Theoretical Informatics. 4th Latin American Symposium, Punta del Este, Uruguay, April 10-14, 2000. Lecture Notes in Comput. Sci. vol. 1776 (2000), Springer, Berlin 126-134
    • (2000) Lecture Notes in Comput. Sci. , vol.1776 , pp. 126-134
    • Corneil, D.G.1    Habib, M.2    Lanlignel, J.-M.3    Reed, B.4    Rotics, U.5
  • 9
    • 0022162058 scopus 로고
    • A linear recognition algorithm for cographs
    • Corneil D.G., Perl Y., and Stewart L.K. A linear recognition algorithm for cographs. SIAM J. Comput. 14 4 (1985) 926-934
    • (1985) SIAM J. Comput. , vol.14 , Issue.4 , pp. 926-934
    • Corneil, D.G.1    Perl, Y.2    Stewart, L.K.3
  • 10
    • 0025398865 scopus 로고
    • The monadic second-order logic of graphs. I. Recognizable sets of finite graphs
    • Courcelle B. The monadic second-order logic of graphs. I. Recognizable sets of finite graphs. Inform. and Comput. 85 1 (1990) 12-75
    • (1990) Inform. and Comput. , vol.85 , Issue.1 , pp. 12-75
    • Courcelle, B.1
  • 11
    • 0028420231 scopus 로고
    • Monadic second-order definable graph transductions: A survey
    • Courcelle B. Monadic second-order definable graph transductions: A survey. Theoret. Comput. Sci. 126 1 (1994) 53-75
    • (1994) Theoret. Comput. Sci. , vol.126 , Issue.1 , pp. 53-75
    • Courcelle, B.1
  • 12
    • 0030169923 scopus 로고    scopus 로고
    • The monadic second-order logic of graphs. X. Linear orderings
    • Courcelle B. The monadic second-order logic of graphs. X. Linear orderings. Theoret. Comput. Sci. 160 1-2 (1996) 87-143
    • (1996) Theoret. Comput. Sci. , vol.160 , Issue.1-2 , pp. 87-143
    • Courcelle, B.1
  • 13
    • 0000090439 scopus 로고    scopus 로고
    • The expression of graph properties and graph transformations in monadic second-order logic
    • World Scientific, River Edge, NJ
    • Courcelle B. The expression of graph properties and graph transformations in monadic second-order logic. Handbook of Graph Grammars and Computing by Graph Transformation vol. 1 (1997), World Scientific, River Edge, NJ 313-400
    • (1997) Handbook of Graph Grammars and Computing by Graph Transformation , vol.1 , pp. 313-400
    • Courcelle, B.1
  • 14
    • 0037453407 scopus 로고    scopus 로고
    • The monadic second-order logic of graphs. XIV. Uniformly sparse graphs and edge set quantifications
    • Courcelle B. The monadic second-order logic of graphs. XIV. Uniformly sparse graphs and edge set quantifications. Theoret. Comput. Sci. 299 1-3 (2003) 1-36
    • (2003) Theoret. Comput. Sci. , vol.299 , Issue.1-3 , pp. 1-36
    • Courcelle, B.1
  • 15
    • 0347415782 scopus 로고    scopus 로고
    • Clique-width of countable graphs: A compactness property
    • Courcelle B. Clique-width of countable graphs: A compactness property. Discrete Math. 266 1-3 (2004) 127-148
    • (2004) Discrete Math. , vol.266 , Issue.1-3 , pp. 127-148
    • Courcelle, B.1
  • 16
    • 27944433098 scopus 로고    scopus 로고
    • The monadic second-order logic of graphs XV: On a conjecture by D. Seese
    • Courcelle B. The monadic second-order logic of graphs XV: On a conjecture by D. Seese. J. Appl. Log. 1 (2006) 79-114
    • (2006) J. Appl. Log. , vol.1 , pp. 79-114
    • Courcelle, B.1
  • 17
    • 0042374663 scopus 로고    scopus 로고
    • B. Courcelle, R.G. Downey, M.R. Fellows, A note on the computability of graph minor obstruction sets for monadic second order ideals, in: Proceedings of the First Japan-New Zealand Workshop on Logic in Computer Science, Auckland, 1997, vol. 3, 1997, pp. 1194-1198 (electronic)
  • 18
    • 0000413488 scopus 로고
    • A logical characterization of the sets of hypergraphs defined by hyperedge replacement grammars
    • Courcelle B., and Engelfriet J. A logical characterization of the sets of hypergraphs defined by hyperedge replacement grammars. Math. Systems Theory 28 6 (1995) 515-552
    • (1995) Math. Systems Theory , vol.28 , Issue.6 , pp. 515-552
    • Courcelle, B.1    Engelfriet, J.2
  • 20
    • 0002015577 scopus 로고    scopus 로고
    • Upper bounds to the clique width of graphs
    • Courcelle B., and Olariu S. Upper bounds to the clique width of graphs. Discrete Appl. Math. 101 1-3 (2000) 77-114
    • (2000) Discrete Appl. Math. , vol.101 , Issue.1-3 , pp. 77-114
    • Courcelle, B.1    Olariu, S.2
  • 21
    • 23944474041 scopus 로고    scopus 로고
    • The recognizability of sets of graphs is a robust property
    • Courcelle B., and Weil P. The recognizability of sets of graphs is a robust property. Theoret. Comput. Sci. 342 2-3 (2005) 173-228
    • (2005) Theoret. Comput. Sci. , vol.342 , Issue.2-3 , pp. 173-228
    • Courcelle, B.1    Weil, P.2
  • 22
    • 0000185443 scopus 로고
    • Tree acceptors and some of their applications
    • Doner J. Tree acceptors and some of their applications. J. Comput. System Sci. 4 (1970) 406-451
    • (1970) J. Comput. System Sci. , vol.4 , pp. 406-451
    • Doner, J.1
  • 24
    • 0031383397 scopus 로고    scopus 로고
    • Logical description of context-free graph languages
    • Engelfriet J., and van Oostrom V. Logical description of context-free graph languages. J. Comput. System Sci. 55 3 (1997) 489-503
    • (1997) J. Comput. System Sci. , vol.55 , Issue.3 , pp. 489-503
    • Engelfriet, J.1    van Oostrom, V.2
  • 25
    • 84945303807 scopus 로고    scopus 로고
    • How to solve NP-hard graph problems on clique-width bounded graphs in polynomial time
    • Graph-Theoretic Concepts in Computer Science. Boltenhagen, 2001, Springer, Berlin
    • Espelage W., Gurski F., and Wanke E. How to solve NP-hard graph problems on clique-width bounded graphs in polynomial time. Graph-Theoretic Concepts in Computer Science. Boltenhagen, 2001. Lecture Notes in Comput. Sci. vol. 2204 (2001), Springer, Berlin 117-128
    • (2001) Lecture Notes in Comput. Sci. , vol.2204 , pp. 117-128
    • Espelage, W.1    Gurski, F.2    Wanke, E.3
  • 26
    • 0002626181 scopus 로고
    • The first order properties of products of algebraic systems
    • Feferman S., and Vaught R.L. The first order properties of products of algebraic systems. Fund. Math. 47 (1959) 57-103
    • (1959) Fund. Math. , vol.47 , pp. 57-103
    • Feferman, S.1    Vaught, R.L.2
  • 27
    • 33751419959 scopus 로고    scopus 로고
    • M.R. Fellows, F.A. Rosamond, U. Rotics, S. Szeider, Proving NP-hardness for clique-width II: Non-approximability of clique-width, Report TR05-081, Revision 01, Electronic Colloquium on Computational Complexity, 2005
  • 28
    • 33748114479 scopus 로고    scopus 로고
    • M.R. Fellows, F.A. Rosamond, U. Rotics, S. Szeider, Clique-width minimization is NP-hard, in: Proceedings of the 38th ACM Symposium on Theory of Computing, 2006, in press
  • 29
    • 0036211275 scopus 로고    scopus 로고
    • Branch-width and well-quasi-ordering in matroids and graphs
    • Geelen J.F., Gerards A.M.H., and Whittle G. Branch-width and well-quasi-ordering in matroids and graphs. J. Combin. Theory Ser. B 84 2 (2002) 270-290
    • (2002) J. Combin. Theory Ser. B , vol.84 , Issue.2 , pp. 270-290
    • Geelen, J.F.1    Gerards, A.M.H.2    Whittle, G.3
  • 30
    • 33751426346 scopus 로고    scopus 로고
    • J.F. Geelen, A.M.H. Gerards, G. Whittle, Excluding a planar graph from GF (q)-representable matroids, Research Report 03-4, School of Mathematical and Computing Sciences, Victoria University of Wellington, 2003
  • 31
    • 0037874823 scopus 로고    scopus 로고
    • On the clique-width of some perfect graph classes
    • Selected papers from the Workshop on Theoretical Aspects of Computer Science (WG 99), Part 1 (Ascona)
    • Golumbic M.C., and Rotics U. On the clique-width of some perfect graph classes. Internat. J. Found. Comput. Sci. 11 3 (2000) 423-443 Selected papers from the Workshop on Theoretical Aspects of Computer Science (WG 99), Part 1 (Ascona)
    • (2000) Internat. J. Found. Comput. Sci. , vol.11 , Issue.3 , pp. 423-443
    • Golumbic, M.C.1    Rotics, U.2
  • 32
    • 32144457687 scopus 로고    scopus 로고
    • On matroid properties definable in the MSO logic
    • Mathematical Foundations of Computer Science, 2003, Springer, Berlin
    • Hliněný P. On matroid properties definable in the MSO logic. Mathematical Foundations of Computer Science, 2003. Lecture Notes in Comput. Sci. vol. 2747 (2003), Springer, Berlin 470-479
    • (2003) Lecture Notes in Comput. Sci. , vol.2747 , pp. 470-479
    • Hliněný, P.1
  • 33
    • 33645920646 scopus 로고    scopus 로고
    • Branch-width, parse trees, and monadic second-order logic for matroids
    • Hliněný P. Branch-width, parse trees, and monadic second-order logic for matroids. J. Combin. Theory Ser. B 96 (2006) 325-351
    • (2006) J. Combin. Theory Ser. B , vol.96 , pp. 325-351
    • Hliněný, P.1
  • 34
    • 32144462149 scopus 로고    scopus 로고
    • Trees, grids, and MSO decidability: From graphs to matroids
    • Hliněný P., and Seese D. Trees, grids, and MSO decidability: From graphs to matroids. Theoret. Comput. Sci. 351 3 (2006) 372-393
    • (2006) Theoret. Comput. Sci. , vol.351 , Issue.3 , pp. 372-393
    • Hliněný, P.1    Seese, D.2
  • 35
    • 84867942957 scopus 로고    scopus 로고
    • Edge dominating set and colorings on graphs with fixed clique-width
    • Kobler D., and Rotics U. Edge dominating set and colorings on graphs with fixed clique-width. Discrete Appl. Math. 126 2-3 (2003) 197-221
    • (2003) Discrete Appl. Math. , vol.126 , Issue.2-3 , pp. 197-221
    • Kobler, D.1    Rotics, U.2
  • 36
    • 1642322895 scopus 로고    scopus 로고
    • Algorithmic uses of the Feferman-Vaught theorem
    • Makowsky J.A. Algorithmic uses of the Feferman-Vaught theorem. Ann. Pure Appl. Logic 126 1-3 (2004) 159-213
    • (2004) Ann. Pure Appl. Logic , vol.126 , Issue.1-3 , pp. 159-213
    • Makowsky, J.A.1
  • 37
    • 33744946823 scopus 로고    scopus 로고
    • Approximating rank-width and clique-width quickly
    • Graph-Theoretic Concepts in Computer Science. Metz, 2005, Springer, Berlin
    • Oum S. Approximating rank-width and clique-width quickly. Graph-Theoretic Concepts in Computer Science. Metz, 2005. Lecture Notes in Comput. Sci. vol. 3787 (2005), Springer, Berlin 49-58
    • (2005) Lecture Notes in Comput. Sci. , vol.3787 , pp. 49-58
    • Oum, S.1
  • 38
    • 33751415556 scopus 로고    scopus 로고
    • S. Oum, Graphs of bounded rank-width, PhD thesis, Princeton University, 2005
  • 39
    • 23244468510 scopus 로고    scopus 로고
    • Rank-width and vertex-minors
    • Oum S. Rank-width and vertex-minors. J. Combin. Theory Ser. B 95 1 (2005) 79-100
    • (2005) J. Combin. Theory Ser. B , vol.95 , Issue.1 , pp. 79-100
    • Oum, S.1
  • 40
    • 33751428139 scopus 로고    scopus 로고
    • S. Oum, Rank-width and well-quasi-ordering, 2005, submitted for publication
  • 41
    • 33751422214 scopus 로고    scopus 로고
    • S. Oum, Approximating rank-width and clique-width quickly. An extended abstract appeared in [37], 2006, submitted for publication
  • 42
    • 32544455938 scopus 로고    scopus 로고
    • Approximating clique-width and branch-width
    • Oum S., and Seymour P. Approximating clique-width and branch-width. J. Combin. Theory Ser. B 96 (2006) 514-528
    • (2006) J. Combin. Theory Ser. B , vol.96 , pp. 514-528
    • Oum, S.1    Seymour, P.2
  • 43
    • 0004061262 scopus 로고
    • Oxford Univ. Press, New York
    • Oxley J.G. Matroid Theory (1992), Oxford Univ. Press, New York
    • (1992) Matroid Theory
    • Oxley, J.G.1
  • 44
    • 0000673493 scopus 로고
    • Graph minors. II. Algorithmic aspects of tree-width
    • Robertson N., and Seymour P. Graph minors. II. Algorithmic aspects of tree-width. J. Algorithms 7 3 (1986) 309-322
    • (1986) J. Algorithms , vol.7 , Issue.3 , pp. 309-322
    • Robertson, N.1    Seymour, P.2
  • 45
    • 0002856269 scopus 로고
    • Graph minors. V. Excluding a planar graph
    • Robertson N., and Seymour P. Graph minors. V. Excluding a planar graph. J. Combin. Theory Ser. B 41 1 (1986) 92-114
    • (1986) J. Combin. Theory Ser. B , vol.41 , Issue.1 , pp. 92-114
    • Robertson, N.1    Seymour, P.2
  • 46
    • 3042806238 scopus 로고
    • Graph minors. IV. Tree-width and well-quasi-ordering
    • Robertson N., and Seymour P. Graph minors. IV. Tree-width and well-quasi-ordering. J. Combin. Theory Ser. B 48 2 (1990) 227-254
    • (1990) J. Combin. Theory Ser. B , vol.48 , Issue.2 , pp. 227-254
    • Robertson, N.1    Seymour, P.2
  • 47
    • 0001227241 scopus 로고
    • Graph minors. X. Obstructions to tree-decomposition
    • Robertson N., and Seymour P. Graph minors. X. Obstructions to tree-decomposition. J. Combin. Theory Ser. B 52 2 (1991) 153-190
    • (1991) J. Combin. Theory Ser. B , vol.52 , Issue.2 , pp. 153-190
    • Robertson, N.1    Seymour, P.2
  • 48
    • 9144239509 scopus 로고    scopus 로고
    • Graph minors. XX. Wagner's conjecture
    • Robertson N., and Seymour P. Graph minors. XX. Wagner's conjecture. J. Combin. Theory Ser. B 92 2 (2004) 325-357
    • (2004) J. Combin. Theory Ser. B , vol.92 , Issue.2 , pp. 325-357
    • Robertson, N.1    Seymour, P.2
  • 49
    • 0001221225 scopus 로고
    • The structure of the models of decidable monadic theories of graphs
    • Seese D. The structure of the models of decidable monadic theories of graphs. Ann. Pure Appl. Logic 53 2 (1991) 169-195
    • (1991) Ann. Pure Appl. Logic , vol.53 , Issue.2 , pp. 169-195
    • Seese, D.1
  • 50
    • 0002614970 scopus 로고
    • Generalized finite automata theory with an application to a decision problem of second-order logic
    • Thatcher J.W., and Wright J.B. Generalized finite automata theory with an application to a decision problem of second-order logic. Math. Systems Theory 2 (1968) 57-81
    • (1968) Math. Systems Theory , vol.2 , pp. 57-81
    • Thatcher, J.W.1    Wright, J.B.2
  • 52
    • 0039301943 scopus 로고
    • k-NLC graphs and polynomial algorithms
    • Wanke E. k-NLC graphs and polynomial algorithms. Discrete Appl. Math. 54 2-3 (1994) 251-266
    • (1994) Discrete Appl. Math. , vol.54 , Issue.2-3 , pp. 251-266
    • Wanke, E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.