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International Workshop on Graph-Theoretic Concepts in Computer Science

WG 2010: Graph Theoretic Concepts in Computer Science pp 184–195Cite as

Colouring Vertices of Triangle-Free Graphs

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 6410)

Abstract

The vertex colouring problem is known to be NP-complete in the class of triangle-free graphs. Moreover, it remains NP-complete even if we additionally exclude a graph F which is not a forest. We study the computational complexity of the problem in (K 3, F)-free graphs with F being a forest. From known results it follows that for any forest F on 5 vertices the vertex colouring problem is polynomial-time solvable in the class of (K 3, F)-free graphs. In the present paper, we show that the problem is also polynomial-time solvable in many classes of (K 3, F)-free graphs with F being a forest on 6 vertices.

Keywords

  • Vertex colouring
  • Triangle-free graphs
  • Polynomial-time algorithm
  • Clique-width

Research supported by the Centre for Discrete Mathematics and Its Applications (DIMAP), University of Warwick.

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Author information

Authors and Affiliations

  1. DIMAP, University of Warwick, Coventry, CV4 7AL, UK

    Konrad Dabrowski, Vadim Lozin, Rajiv Raman & Bernard Ries

Authors
  1. Konrad Dabrowski
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  2. Vadim Lozin
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  3. Rajiv Raman
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  4. Bernard Ries
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Athens, Panepistimioupolis, GR-15784, Athens, Greece

    Dimitrios M. Thilikos

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Dabrowski, K., Lozin, V., Raman, R., Ries, B. (2010). Colouring Vertices of Triangle-Free Graphs. In: Thilikos, D.M. (eds) Graph Theoretic Concepts in Computer Science. WG 2010. Lecture Notes in Computer Science, vol 6410. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16926-7_18

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  • DOI: https://doi.org/10.1007/978-3-642-16926-7_18

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