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The complexity of colouring circle graphs

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STACS 92 (STACS 1992)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 577))

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Abstract

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.

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Author information

Authors and Affiliations

  1. Fachbereich 17, University of Paderborn, Warburger Straße 100, 4790, Paderborn, Germany

    Walter Unger

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  1. Walter Unger
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Alain Finkel Matthias Jantzen

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© 1992 Springer-Verlag Berlin Heidelberg

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Unger, W. (1992). The complexity of colouring circle graphs. In: Finkel, A., Jantzen, M. (eds) STACS 92. STACS 1992. Lecture Notes in Computer Science, vol 577. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55210-3_199

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  • DOI: https://doi.org/10.1007/3-540-55210-3_199

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55210-9

  • Online ISBN: 978-3-540-46775-5

  • eBook Packages: Springer Book Archive

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