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

Author

Listed:
  • Zuosong Liang

    (Qufu Normal University)

  • Erfang Shan

    (Shanghai University
    Shanghai University)

  • Yuzhong Zhang

    (Qufu Normal University)

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.

Suggested Citation

  • Zuosong Liang & Erfang Shan & Yuzhong Zhang, 2017. "A linear-time algorithm for clique-coloring problem in circular-arc graphs," Journal of Combinatorial Optimization, Springer, vol. 33(1), pages 147-155, January.
    • Handle: RePEc:spr:jcomop:v:33:y:2017:i:1:d:10.1007_s10878-015-9941-3
    DOI: 10.1007/s10878-015-9941-3
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