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

  • Flavia Bonomo
  • Guillermo Durán
  • Francisco Soulignac
  • Gabriel Sueiro
Original 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. 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.

Keywords

Complements of forests Coordinated graphs Line graphs Perfect graphs 

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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Flavia Bonomo
    • 1
    • 4
  • Guillermo Durán
    • 2
    • 3
    • 4
  • Francisco Soulignac
    • 1
  • Gabriel Sueiro
    • 1
  1. 1.Departamento de Computación, Facultad de Ciencias Exactas y NaturalesUniversidad de Buenos AiresBuenos AiresArgentina
  2. 2.Departamento de Ingeniería Industrial, Facultad de Ciencias Físicas y MatemáticasUniversidad de ChileSantiagoChile
  3. 3.Departamento de Matemática, Facultad de Ciencias Exactas y NaturalesUniversidad de Buenos AiresBuenos AiresArgentina
  4. 4.CONICETBuenos AiresArgentina

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