A linear-time algorithm for clique-coloring problem in circular-arc graphs

Zuosong Liang, Erfang Shan () and Yuzhong Zhang
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Zuosong Liang: Qufu Normal University
Erfang Shan: Shanghai University
Yuzhong Zhang: Qufu Normal University

Journal of Combinatorial Optimization, 2017, vol. 33, issue 1, No 10, 147-155

Abstract: 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.

Keywords: Clique-coloring; Circular-arc graph; Linear time algorithm; 05C15; 05C69 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10878-015-9941-3

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