On the k-colouring of circle-graphs

  • Walter Unger
Contributed Papers Algorithms

DOI: 10.1007/BFb0035832

Part of the Lecture Notes in Computer Science book series (LNCS, volume 294)
Cite this paper as:
Unger W. (1988) On the k-colouring of circle-graphs. In: Cori R., Wirsing M. (eds) STACS 88. STACS 1988. Lecture Notes in Computer Science, vol 294. Springer, Berlin, Heidelberg

Abstract

It is shown that the k-colouring problem for the class of circle graphs is NP-complete for k at least four. Until now this problem was still open. For circle graphs with maximum clique size k a 2k-colouring is always possible and can be found in O(n2). This provides an approximation algorithm with a factor two. Further it is proven that the k-colouring problem for circle graphs is solvable in polynomial time if the degree is bounded. The complexity of the 3-colouring problem for circle graphs remains open.

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Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • Walter Unger
    • 1
  1. 1.Fachbereich 17 Universität-GH PaderbornPaderbornWest-Germany

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