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

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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.

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Authors and Affiliations

  1. Departamento de Computación, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, pab. I (1428), Buenos Aires, Argentina

    Flavia Bonomo, Francisco Soulignac & Gabriel Sueiro

  2. Departamento de Ingeniería Industrial, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Santiago, Chile

    Guillermo Durán

  3. Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, Argentina

    Guillermo Durán

  4. CONICET, Buenos Aires, Argentina

    Flavia Bonomo & Guillermo Durán

Authors
  1. Flavia Bonomo
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  2. Guillermo Durán
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  3. Francisco Soulignac
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  4. Gabriel Sueiro
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Corresponding author

Correspondence to Flavia Bonomo.

Additional information

F. Bonomo, F. Soulignac, and G. Sueiro’s research partially supported by UBACyT Grant X184 (Argentina), and CNPq under PROSUL project Proc. 490333/2004-4 (Brazil).

The research of G. Durán is partially supported by FONDECyT Grant 1080286 and Millennium Science Institute “Complex Engineering Systems” (Chile), and CNPq under PROSUL project Proc. 490333/2004-4 (Brazil).

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Bonomo, F., Durán, G., Soulignac, F. et al. Partial characterizations of coordinated graphs: line graphs and complements of forests. Math Meth Oper Res 69, 251–270 (2009). https://doi.org/10.1007/s00186-008-0257-2

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  • DOI: https://doi.org/10.1007/s00186-008-0257-2

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