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(n 2). 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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© 1988 Springer-Verlag Berlin Heidelberg
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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. https://doi.org/10.1007/BFb0035832
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DOI: https://doi.org/10.1007/BFb0035832
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