Abstract
A maximal clique of G is a clique not properly contained in any other clique. A k-clique-coloring of a graph G is an assignment of k colors to the vertices of G such that no maximal clique with at least two vertices is monochromatic. The smallest integer k admitting a k-clique-coloring of G is called clique-coloring number of G. Cerioli and Korenchendler (Electron Notes Discret Math 35:287–292, 2009) showed that there is a polynomial-time algorithm to solve the clique-coloring problem in circular-arc graphs and asked whether there exists a linear-time algorithm to find an optimal clique-coloring in circular-arc graphs or not. In this paper we present a linear-time algorithm of the optimal clique-coloring in circular-arc graphs.
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Acknowledgments
This research was partially supported by the National Nature Science Foundation of China (No. 11171207 and 11426144) and the Nature Science Foundation of Shandong Province, China (No. ZR2014AQ008).
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Liang, Z., Shan, E. & Zhang, Y. A linear-time algorithm for clique-coloring problem in circular-arc graphs. J Comb Optim 33, 147–155 (2017). https://doi.org/10.1007/s10878-015-9941-3
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DOI: https://doi.org/10.1007/s10878-015-9941-3