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On edge orienting methods for graph coloring

Author

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  • Bernard Gendron

    (Université de Montréal)

  • Alain Hertz

    (École Polytechnique)

  • Patrick St-Louis

    (Université de Montréal)

Abstract

We consider the problem of orienting the edges of a graph so that the length of a longest path in the resulting digraph is minimum. As shown by Gallai, Roy and Vitaver, this edge orienting problem is equivalent to finding the chromatic number of a graph. We study various properties of edge orienting methods in the context of local search for graph coloring. We then exploit these properties to derive four tabu search algorithms, each based on a different neighborhood. We compare these algorithms numerically to determine which are the most promising and to give potential research directions.

Suggested Citation

  • Bernard Gendron & Alain Hertz & Patrick St-Louis, 2007. "On edge orienting methods for graph coloring," Journal of Combinatorial Optimization, Springer, vol. 13(2), pages 163-178, February.
    • Handle: RePEc:spr:jcomop:v:13:y:2007:i:2:d:10.1007_s10878-006-9019-3
    DOI: 10.1007/s10878-006-9019-3
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    References listed on IDEAS

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    1. Valmir C. Barbosa & Carlos A.G. Assis & Josina O. Do Nascimento, 2004. "Two Novel Evolutionary Formulations of the Graph Coloring Problem," Journal of Combinatorial Optimization, Springer, vol. 8(1), pages 41-63, March.
    2. Peter J. M. van Laarhoven & Emile H. L. Aarts & Jan Karel Lenstra, 1992. "Job Shop Scheduling by Simulated Annealing," Operations Research, INFORMS, vol. 40(1), pages 113-125, February.
    3. Anuj Mehrotra & Michael A. Trick, 1996. "A Column Generation Approach for Graph Coloring," INFORMS Journal on Computing, INFORMS, vol. 8(4), pages 344-354, November.
    4. J. Randall Brown, 1972. "Chromatic Scheduling and the Chromatic Number Problem," Management Science, INFORMS, vol. 19(4-Part-1), pages 456-463, December.
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    Cited by:

    1. Peter Damaschke, 2019. "Parameterized Mixed Graph Coloring," Journal of Combinatorial Optimization, Springer, vol. 38(2), pages 362-374, August.

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