Colored Modular and Split Decompositions of Graphs with Applications to Trigraphs

  • Michel Habib
  • Antoine MamcarzEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8747)


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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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.LIAFA UMR 7089CNRS and Université Paris Diderot - Paris 7ParisFrance

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