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More Results on Clique-chromatic Numbers of Graphs with No Long Path

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Discrete and Computational Geometry and Graphs (JCDCGG 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8845))

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Abstract

The clique-chromatic number of a graph is the least number of colors on the vertices of the graph so that no maximal clique of size at least two is monochromatic. In 2003, Gravier, Hoang, and Maffray have shown that, for any graph \(F\), the class of \(F\)-free graphs has a bounded clique-chromatic number if and only if \(F\) is a vertex-disjoint union of paths, and they give an upper bound for all such cases. In this paper, their bounds for \(F=P_2+kP_1\) and \(F=P_3+kP_1\) with \(k \ge 3\) are significantly reduced to \(k+1\) and \(k+2\) respectively, and sharp bounds are given for some subclasses.

Tanawat Wichianpaisarn—Partially supported by His Royal Highness Crown Prince Maha Vajiralongkorn Fund.

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Correspondence to Chariya Uiyyasathian .

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Wichianpaisarn, T., Uiyyasathian, C. (2014). More Results on Clique-chromatic Numbers of Graphs with No Long Path. In: Akiyama, J., Ito, H., Sakai, T. (eds) Discrete and Computational Geometry and Graphs. JCDCGG 2013. Lecture Notes in Computer Science(), vol 8845. Springer, Cham. https://doi.org/10.1007/978-3-319-13287-7_16

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  • DOI: https://doi.org/10.1007/978-3-319-13287-7_16

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