On the k-colouring of circle-graphs

  • Walter Unger
Contributed Papers Algorithms
Part of the Lecture Notes in Computer Science book series (LNCS, volume 294)


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.


Polynomial Time Planar Graph Undirected Graph Chordal Graph Boolean Expression 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

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

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