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Colored Modular and Split Decompositions of Graphs with Applications to Trigraphs

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Graph-Theoretic Concepts in Computer Science (WG 2014)

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Abstract

We introduce the colored decompositions framework, in which vertices of the graph can be equipped with colors, and in which the goal is to find decompositions of this graph that do not separate the color classes. In this paper, we give two linear time algorithms for the colored modular and split decompositions of graphs, and we apply them to give linear time algorithms for the modular and split decompositions of trigraphs, which improves a result of Thomassé, Trotignon and Vuskovic (2013). As a byproduct, we introduce the non-separating families that allow us to prove that those two decompositions have the same properties on graphs and on trigraphs.

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Authors and Affiliations

  1. LIAFA UMR 7089, CNRS and Université Paris Diderot - Paris 7, 75205, Paris, France

    Michel Habib & Antoine Mamcarz

Authors
  1. Michel Habib
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  2. Antoine Mamcarz
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Correspondence to Antoine Mamcarz .

Editor information

Editors and Affiliations

  1. LITA, Université de Lorraine, Metz Cedex 01, France

    Dieter Kratsch

  2. Université d'Orléans, Orléans, France

    Ioan Todinca

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Habib, M., Mamcarz, A. (2014). Colored Modular and Split Decompositions of Graphs with Applications to Trigraphs. In: Kratsch, D., Todinca, I. (eds) Graph-Theoretic Concepts in Computer Science. WG 2014. Lecture Notes in Computer Science, vol 8747. Springer, Cham. https://doi.org/10.1007/978-3-319-12340-0_22

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  • DOI: https://doi.org/10.1007/978-3-319-12340-0_22

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-12339-4

  • Online ISBN: 978-3-319-12340-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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