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NP-hardness of the recognition of coordinated graphs

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  • Francisco Soulignac
  • Gabriel Sueiro

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

Suggested Citation

  • Francisco Soulignac & Gabriel Sueiro, 2009. "NP-hardness of the recognition of coordinated graphs," Annals of Operations Research, Springer, vol. 169(1), pages 17-34, July.
    • Handle: RePEc:spr:annopr:v:169:y:2009:i:1:p:17-34:10.1007/s10479-008-0392-4
    DOI: 10.1007/s10479-008-0392-4
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