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On Split-Coloring Problems

Author

Listed:
  • T. Ekim

    (Ecole Polytechnique Fédérale de Lausanne)

  • D. Werra

    (Ecole Polytechnique Fédérale de Lausanne)

Abstract

We study a new coloring concept which generalizes the classical vertex coloring problem in a graph by extending the notion of stable sets to split graphs. First of all, we propose the packing problem of finding the split graph of maximum size where a split graph is a graph G = (V,E) in which the vertex set V can be partitioned into a clique K and a stable set S. No condition is imposed on the edges linking vertices in S to the vertices in K. This maximum split graph problem gives rise to an associated partitioning problem that we call the split-coloring problem. Given a graph, the objective is to cover all his vertices by a least number of split graphs. Definitions related to this new problem are introduced. We mention some polynomially solvable cases and describe open questions on this area.

Suggested Citation

  • T. Ekim & D. Werra, 2005. "On Split-Coloring Problems," Journal of Combinatorial Optimization, Springer, vol. 10(3), pages 211-225, November.
    • Handle: RePEc:spr:jcomop:v:10:y:2005:i:3:d:10.1007_s10878-005-4103-7
    DOI: 10.1007/s10878-005-4103-7
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    Cited by:

    1. Demange, Marc & Ekim, TInaz & de Werra, Dominique, 2009. "A tutorial on the use of graph coloring for some problems in robotics," European Journal of Operational Research, Elsevier, vol. 192(1), pages 41-55, January.

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