Partial characterizations of coordinated graphs: line graphs and complements of forests

Flavia Bonomo (), Guillermo Durán (), Francisco Soulignac () and Gabriel Sueiro ()

Mathematical Methods of Operations Research, 2009, vol. 69, issue 2, 270 pages

Abstract: 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 is equal to 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 list of minimal forbidden induced subgraphs for the class of coordinated graphs is not known. In this paper, we present a partial result in this direction, that is, we characterize coordinated graphs by minimal forbidden induced subgraphs when the graph is either a line graph, or the complement of a forest. Copyright Springer-Verlag 2009

Keywords: Complements of forests; Coordinated graphs; Line graphs; Perfect graphs (search for similar items in EconPapers)
Date: 2009
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DOI: 10.1007/s00186-008-0257-2

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