On the k-colouring of circle-graphs
- Cite this paper as:
- 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
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.
Unable to display preview. Download preview PDF.