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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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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

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-16925-0

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