The complexity of colouring circle graphs

Extended abstract
  • Walter Unger
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 577)


We study the complexity of the colouring problem for circle graphs. We will solve the two open questions of [Un88], where first results were presented.
  1. 1.

    Here we will present an algorithm which solves the 3-colouring problem of circle graphs in time O(nlog(n)). In [Un88] we showed that the 4-colouring problem for circle graphs is NP-complete.

  2. 2.

    If the largest clique of a circle graph has size k then the 2·k−1-colouring is NP-complete. Such circle graphs are 2·k-colourable [Un88].


Further results and improvements of [Un88] complete the knowledge of the complexity of the colouring problem of circle graphs.


algorithms and data structures computational complexity 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Walter Unger
    • 1
  1. 1.Fachbereich 17University of PaderbornPaderbornGermany

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