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...
| Autores: | , , , |
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| 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 |
| 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. |
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