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NP-hardness of the recognition of coordinated graphs

  • Francisco J. Soulignac
  • Gabriel Sueiro
Article

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.

Keywords

Computational complexity Coordinated graph recognition {gem, C4, odd hole}-free graphs NP-complete problems 

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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Departamento de Computación, Facultad de Ciencias Exactas y NaturalesUniversidad de Buenos AiresBuenos AiresArgentina

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