Colouring Vertices of Triangle-Free Graphs

  • Konrad Dabrowski
  • Vadim Lozin
  • Rajiv Raman
  • Bernard Ries
Part of the Lecture Notes in Computer Science book series (LNCS, 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 (K3, 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 (K3, F)-free graphs. In the present paper, we show that the problem is also polynomial-time solvable in many classes of (K3, F)-free graphs with F being a forest on 6 vertices.

Keywords

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

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Konrad Dabrowski
    • 1
  • Vadim Lozin
    • 1
  • Rajiv Raman
    • 1
  • Bernard Ries
    • 1
  1. 1.DIMAPUniversity of WarwickCoventryUK

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