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.
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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.
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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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© 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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