Abstract
A circle graph is the intersection graph of chords drawn in a circle. The best-known general upper bound on the chromatic number of circle graphs with clique number k is \(50 \cdot {2}^{k}\). We prove a stronger bound of 2k−1 for graphs in a simpler subclass of circle graphs, called clean graphs. Based on this result, we prove that the chromatic number of every circle graph with clique number at most 3 is at most 38.
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Acknowledgements
The first author’s research is supported in part by NSF Grant DMS-0965587 and by Grant 09-01-00244-a of the Russian Foundation for Basic Research.
The second author acknowledges support of the National Science Foundation through a fellowship funded by Grant EMSW21-MCTP, ”Research Experience for Graduate Students” (NSF DMS 08-38434).
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Kostochka, A.V., Milans, K.G. (2013). Coloring Clean and K 4-Free Circle Graphs. In: Pach, J. (eds) Thirty Essays on Geometric Graph Theory. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0110-0_21
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DOI: https://doi.org/10.1007/978-1-4614-0110-0_21
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