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 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 cliqueperfect 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. Key words: Clique-perfect graphs, coordinated graphs, {gem,W4,bull}-free graphs, paw-fre...

• Type: Journal
• Year: 2008
• Where: ENDM
• Authors: Flavia Bonomo, Guillermo Durán, Francisco J. Soulignac, Gabriel Sueiro
• Keywords: Cliques, ENDM 2008, Maximum Clique-independent Set, Perfect Graphs