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Coloring a Graph Using Split Decomposition

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Graph-Theoretic Concepts in Computer Science (WG 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3353))

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Abstract

We show how to use split decomposition to compute the weighted clique number and the chromatic number of a graph and we apply these results to some classes of graphs. In particular we present an O(n 2 m) algorithm to compute the chromatic number for all those graphs having a split decomposition in which every prime graph is an induced subgraph of either a C k or a \(\overline{C_k}\) for some k≥ 3.

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Author information

Authors and Affiliations

  1. Laboratoire d’Informatique Théorique et Appliquée, Université de Metz, 57045, Metz Cedex 01, France

    Michaël Rao

Authors
  1. Michaël Rao
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Editor information

Editors and Affiliations

  1. Department of Computer Science, ETH Zurich, ETH Zentrum, CH-8022, Zurich, Switzerland

    Juraj Hromkovič

  2. Department of Computer Science, RWTH Aachen, Chair of Computer Science III, Aachen, Germany

    Manfred Nagl

  3. Department of Computer Science III, RWTH Aachen University, Ahornstra{ß}e 55, 52074, Aachen, Germany

    Bernhard Westfechtel

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© 2004 Springer-Verlag Berlin Heidelberg

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Rao, M. (2004). Coloring a Graph Using Split Decomposition. In: Hromkovič, J., Nagl, M., Westfechtel, B. (eds) Graph-Theoretic Concepts in Computer Science. WG 2004. Lecture Notes in Computer Science, vol 3353. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30559-0_11

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  • DOI: https://doi.org/10.1007/978-3-540-30559-0_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-24132-4

  • Online ISBN: 978-3-540-30559-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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