Partial characterizations of clique-perfect and coordinated graphs: Superclasses of triangle-free graphs

A graph G is clique-perfect if the cardinality of a maximum clique-independent set of H equals the cardinality of a minimum clique-transversal of H, for every induced subgraph H of G. A graph G is coordinated if the minimum number of colors that can be assigned to the cliques of H in such a way that...

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Detalles Bibliográficos
Autores: Bonomo, F., Durán, G., Soulignac, F., Sueiro, G.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2009
País:Argentina
Institución:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
Repositorio:Biblioteca Digital (UBA-FCEN)
Idioma:inglés
OAI Identifier:paperaa:paper_0166218X_v157_n17_p3511_Bonomo
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_0166218X_v157_n17_p3511_Bonomo
Access Level:acceso abierto
Palabra clave:Clique-perfect graphs
Coordinated graphs
Paw-free graphs
Perfect graphs
Triangle-free graphs
{gem, W4, bull}-free graphs
{gem, W<sub>4</sub>, bull}-free graphs
Gems
Graph theory
Descripción
Sumario:A graph G is clique-perfect if the cardinality of a maximum clique-independent set of H equals the cardinality of a minimum clique-transversal of H, for every induced subgraph H of G. A graph G is coordinated if the minimum number of colors that can be assigned to the cliques of H in such a way that no two cliques with non-empty intersection receive the same color equals the maximum number of cliques of H with a common vertex, for every induced subgraph H of G. Coordinated graphs are a subclass of perfect graphs. The complete lists of minimal forbidden induced subgraphs for the classes of clique-perfect and coordinated graphs are not known, but some partial characterizations have been obtained. In this paper, we characterize clique-perfect and coordinated graphs by minimal forbidden induced subgraphs when the graph is either paw-free or {gem, W4, bull}-free, both superclasses of triangle-free graphs. © 2009 Elsevier B.V. All rights reserved.