NP-hardness of the recognition of coordinated graphs

Francisco Soulignac () and Gabriel Sueiro ()

Annals of Operations Research, 2009, vol. 169, issue 1, 17-34

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. In previous works, polynomial time algorithms were found for recognizing coordinated graphs within some classes of graphs. In this paper we prove that the recognition problem for coordinated graphs is NP-hard, and it is NP-complete even when restricted to the class of {gem, C 4 , odd hole}-free graphs with maximum degree four, maximum clique size three and at most three cliques sharing a common vertex. Copyright Springer Science+Business Media, LLC 2009

Keywords: Computational complexity; Coordinated graph recognition; {gem; C 4; odd hole}-free graphs; NP-complete problems (search for similar items in EconPapers)
Date: 2009
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DOI: 10.1007/s10479-008-0392-4

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