Artículo

Bonomo, F.; Durán, G.; Safe, M.D.; Wagler, A.K. "Clique-perfectness of complements of line graphs" (2015) Discrete Applied Mathematics. 186(1):19-44
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Abstract:

A graph is clique-perfect if the maximum number of pairwise disjoint maximal cliques equals the minimum number of vertices intersecting all maximal cliques for each induced subgraph. In this work, we give necessary and sufficient conditions for the complement of a line graph to be clique-perfect and an O (n2) -time algorithm to recognize such graphs. These results follow from a characterization and a linear-time recognition algorithm for matching-perfect graphs, which we introduce as graphs where the maximum number of pairwise edge-disjoint maximal matchings equals the minimum number of edges intersecting all maximal matchings for each subgraph. Thereby, we completely describe the linear and circular structure of the graphs containing no bipartite claw, from which we derive a structure theorem for all those graphs containing no bipartite claw that are Class 2 with respect to edge-coloring. © 2015 Elsevier B.V. All rights reserved.

Registro:

Documento: Artículo
Título:Clique-perfectness of complements of line graphs
Autor:Bonomo, F.; Durán, G.; Safe, M.D.; Wagler, A.K.
Filiación:CONICET, Departamento de Computación, Universidad de Buenos Aires, Argentina
Instituto de Cálculo, Departamento de Matemática, Universidad de Buenos Aires, Argentina
Departamento de Ingeniería Industrial, FCFM, Universidad de Chile, Chile
Instituto de Ciencias, Universidad Nacional de General Sarmiento, Argentina
CNRS, LIMOS, Université Blaise Pascal, Clermont-Ferrand, France
Palabras clave:Clique-perfect graphs; Edge-coloring; Line graphs; Matchings; Graphic methods; All maximal cliques; Circular structures; Edge coloring; Induced subgraphs; Line graph; Matchings; Perfect graph; Recognition algorithm; Graph theory
Año:2015
Volumen:186
Número:1
Página de inicio:19
Página de fin:44
DOI: http://dx.doi.org/10.1016/j.dam.2015.01.012
Título revista:Discrete Applied Mathematics
Título revista abreviado:Discrete Appl Math
ISSN:0166218X
CODEN:DAMAD
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0166218X_v186_n1_p19_Bonomo

Referencias:

  • Balachandran, V., Nagavamsi, P., Pandu Rangan, C., Clique transversal and clique independence on compar ability graphs (1996) Inform. Process. Lett., 58, pp. 181-184
  • Beineke, L.W., Fiorini, S., On small graphs critical with respect to edge colourings (1976) Discrete Math., 16, pp. 109-121
  • Berge, C., Färbung von Graphen, deren sämtliche beziehungsweise, deren ungerade Kreise starr sind (Zusammenfassung) (1961) Math.-Naturwiss. Reihe, 10, pp. 114-115. , Wiss.Z. Martin-Luther-Univ. Halle-Wittenberg
  • Berge, C., Hypergraphs: Combinatorics of finite sets (1989) North-Holland Mathematical Library, 45. , North-Holland, Amsterdam
  • Berge, C., Las Vergnas, M., Sur un théorème du type könig pour hypergraphes (1970) Ann. New York Acad. Sci., 175, pp. 32-40
  • Bodlaender, H.L., A linear-time algorithm for finding tree-decompositions of small treewidth (1996) SIAM J. Comput., 25, pp. 1305-1317
  • Bonomo, F., (2005) Onsubclasses and Variations of Perfect Graphs, , Doctoral Dissertation, Departamento deComputación, FCEyN, Universidad de Buenos Aires, Buenos Aires, Argentina
  • Bonomo, F., Chudnovsky, M., Durán, G., Partial characterizations of clique-perfect graphs I: Subclasses of claw-free graphs (2008) Discrete Appl. Math., 156, pp. 1058-1082
  • Bonomo, F., Chudnovsky, M., Durán, G., Partial characterizations of clique-perfect graphs II: Diamond-free and helly circular-arc graphs (2009) Discrete Math., 309, pp. 3485-3499
  • Bonomo, F., Durán, G., Safe, M.D., Wagler, A.K., Clique-perfectness of complements of line graphs (2011) Electron. Notes Discrete Math., 37, pp. 327-332
  • Bonomo, F., Durán, G., Soulignac, F., Sueiro, G., Partial characterizations of clique-perfect and coordinated graphs: Superclasses of triangle-free graphs (2009) Discrete Appl. Math., 157, pp. 3511-3518
  • Borie, R.B., Gary Parker, R., Tovey, C.A., Automatic generation of linear-time algorithms from predicate calculus descriptions of problems on recursively constructed graph families (1992) Algorithmica, 7, pp. 555-581
  • Brandstädt, A., Chepoi, V.D., Dragan, F.F., Clique r-domination and clique r-packing problems on dually chordal graphs (1997) SIAM J. Discrete Math., 10, pp. 109-127
  • Brandstädt, A., Chepoi, V.D., Dragan, F.F., Voloshin, V., Dually chordal graphs (1998) SIAM J. Discrete Math., 11, pp. 437-455
  • Brandstädt, A., Dragan, F.F., On linear and circular structure of (claw, net)-free graphs (2003) Discrete Appl. Math., 129, pp. 285-303
  • Cariolaro, D., Cariolaro, G., Colouring the petals of a graph (2003) Electron. J. Combin., 10, p. R6
  • Chang, M., Farber, M., Tuza, Z., Algorithmic aspects of neighbourhood numbers (1993) SIAM J. Discrete Math., 6, pp. 24-29
  • Chudnovsky, M., Cornuéjols, G.P., Liu, X., Seymour, P.D., Vušković, K., Recognizing berge graphs (2005) Combinatorica, 25, pp. 143-186
  • Chudnovsky, M., Robertson, N., Seymour, P.D., Thomas, R., The strong perfect graph theorem (2006) Ann. Math., 164, pp. 51-229
  • Courcelle, B., The monadic second-order logic of graphs. I. Recognizable sets of finite graphs (1990) Inform. and Comput., 85, pp. 12-75
  • Courcelle, B., Engelfriet, J., Graph structure and monadic second-order logic: A language-theoretic approach (2012) Encyclopedia of Mathematics and its Applications, 138. , Cambridge University Press, Cambridge
  • Dahlhaus, E., Manuel, P.D., Miller, M., Maximum h-colourable subgraph problem in balanced graphs (1998) Inform. Process. Lett., 65, pp. 301-303
  • Diestel, R., Graph theory (2010) Graduate Texts in Mathematics, 173. , fourth edition Springer-Verlag, Heidelberg
  • Durán, G., Lin, M.C., Mera, S., Szwarcfiter, J.L., Algorithms for clique-independent sets on subclasses of circular-arc graphs (2006) Discrete Appl. Math., 154, pp. 1783-1790
  • Durán, G., Lin, M.C., Mera, S., Szwarcfiter, J.L., Algorithms for finding clique-transversals of graphs (2008) Ann. Oper. Res., 157, pp. 37-45
  • Durán, G., Lin, M.C., Szwarcfiter, J.L., On clique-transversal and clique-independent sets (2002) Ann. Oper. Res., 116, pp. 71-77
  • Egerváry, J., Matrixok kombinatorikus tulajdonságairól (1931) Mat. Fiz. Lapok, 38, pp. 16-28. , (In Hungarian)
  • Erdos, P., Gallai, T., Tuza, Z., Covering the cliques of a graph with vertices (1992) Discrete Math., 108, pp. 279-289
  • Fulkerson, D., Blocking and anti-blocking pairs of polyhedra (1971) Math. Program., 1, pp. 168-194
  • Guruswami, V., Pandu Rangan, C., Algorithmic aspects of clique-transversal and clique-independent sets (2000) Discrete Appl. Math., 100, pp. 183-202
  • Hall, P., On representatives of subsets (1935) J. Lond. Math. Soc., 10, pp. 26-30
  • Harary, F., Schwenk, A.J., The number of caterpillars (1973) Discrete Math., 6, pp. 359-365
  • Harary, F., Schwenk, A.J., Trees with hamiltonian square (1971) Mathematika, 18, pp. 138-140
  • Hilton, A.J.W., Zhao, C., The chromatic index of a graph whose core has maximum degree two (1992) Discrete Math., 101, pp. 135-147
  • Hoyler, I., The NP-completeness of edge-coloring (1981) SIAM J. Comput., 10, pp. 718-720
  • Konig, D., Graphok és matrixok (1931) Mat. Fiz. Lapok, 38, pp. 116-119. , (In Hungarian)
  • Lee, C.M., Chang, M.S., Distance-hereditary graphs are clique-perfect (2006) Discrete Appl. Math., 154, pp. 525-536
  • Lehel, J., Tuza, Z., Neighborhood perfect graphs (1986) Discrete Math., 61, pp. 93-101
  • Lehot, P.G.H., An optimal algorithm to detect a line graph and output its root graph (1974) J. ACM, 21, pp. 569-575
  • Lovász, L., Normal hypergraphs and the perfect graph conjecture (1972) Discrete Math., 2, pp. 253-267
  • Lucchesi, C., Picinin De Mello, C., Szwarcfiter, J.L., On clique-complete graphs (1998) Discrete Math., 183, pp. 247-254
  • Maffray, F., Kernels in perfect line-graphs (1992) J. Combin. Theory Ser. B, 55, pp. 1-8
  • Parthasarathy, K., Ravindra, G., The strong perfect-graph conjecture is true for K1, 3-free graphs (1976) J. Combin. Theory Ser. B, 21, pp. 212-223
  • Robertson, N., Seymour, P.D., Graph minors. I. Excluding a forest (1983) J. Combin. Theory Ser. B, 35, pp. 39-61
  • Robertson, N., Seymour, P.D., Graph minors. II. Algorithmic aspects of tree-width (1986) J. Algorithms, 7, pp. 309-322
  • Roussopoulos, N.D., A max{m, n} algorithm for determining the graph H from its line graph G (1973) Inform. Process. Lett., 2, pp. 108-112
  • Tarjan, R.E., Depth-first search and linear graph algorithms (1972) SIAM J. Comput., 1, pp. 146-160
  • Vizing, V.G., On an estimate of the chromatic class of a p-graph (1964) Metody Diskret. Anal., 3, pp. 25-30. , (In Russian)
  • Vizing, V.G., Critical graphs with given chromatic class (1965) Diskret. Analiz, 5, pp. 9-17. , (In Russian)
  • West, D.B., (2001) Introduction to Graph Theory, , second ed., Prentice-Hall, Upper Saddle River, NJ
  • Whitney, H., Congruent graphs and the connectivity of graphs (1932) Amer. J. Math., 54, pp. 150-168
  • Zhou, X., Nakano, S., Nishizeki, T., Edge-coloring partial k-trees (1996) J. Algorithms, 21, pp. 598-617

Citas:

---------- APA ----------
Bonomo, F., Durán, G., Safe, M.D. & Wagler, A.K. (2015) . Clique-perfectness of complements of line graphs. Discrete Applied Mathematics, 186(1), 19-44.
http://dx.doi.org/10.1016/j.dam.2015.01.012
---------- CHICAGO ----------
Bonomo, F., Durán, G., Safe, M.D., Wagler, A.K. "Clique-perfectness of complements of line graphs" . Discrete Applied Mathematics 186, no. 1 (2015) : 19-44.
http://dx.doi.org/10.1016/j.dam.2015.01.012
---------- MLA ----------
Bonomo, F., Durán, G., Safe, M.D., Wagler, A.K. "Clique-perfectness of complements of line graphs" . Discrete Applied Mathematics, vol. 186, no. 1, 2015, pp. 19-44.
http://dx.doi.org/10.1016/j.dam.2015.01.012
---------- VANCOUVER ----------
Bonomo, F., Durán, G., Safe, M.D., Wagler, A.K. Clique-perfectness of complements of line graphs. Discrete Appl Math. 2015;186(1):19-44.
http://dx.doi.org/10.1016/j.dam.2015.01.012