Partial characterizations of clique-perfect graphs I: Subclasses of claw-free graphs

A clique-transversal of a graph G is a subset of vertices that meets all the cliques of G. A clique-independent set is a collection of pairwise vertex-disjoint cliques. The clique-transversal number and clique-independence number of G are the sizes of a minimum clique-transversal and a maximum cliqu...

Descripción completa

Detalles Bibliográficos
Autores: Bonomo, F., Chudnovsky, M., Durán, G.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2008
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_v156_n7_p1058_Bonomo
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_0166218X_v156_n7_p1058_Bonomo
Access Level:acceso abierto
Palabra clave:Claw-free graphs
Clique-perfect graphs
Hereditary clique-Helly graphs
Line graphs
Perfect graphs
Image processing
Mathematical models
Number theory
Problem solving
Set theory
Claw free graphs
Clique perfect graphs
Graph theory
Descripción
Sumario:A clique-transversal of a graph G is a subset of vertices that meets all the cliques of G. A clique-independent set is a collection of pairwise vertex-disjoint cliques. The clique-transversal number and clique-independence number of G are the sizes of a minimum clique-transversal and a maximum clique-independent set of G, respectively. A graph G is clique-perfect if these two numbers are equal for every induced subgraph of G. The list of minimal forbidden induced subgraphs for the class of clique-perfect graphs is not known. In this paper, we present a partial result in this direction; that is, we characterize clique-perfect graphs by a restricted list of forbidden induced subgraphs when the graph belongs to two different subclasses of claw-free graphs. © 2007 Elsevier B.V. All rights reserved.