On Split-Coloring Problems

T. Ekim () and D. Werra ()
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T. Ekim: Ecole Polytechnique Fédérale de Lausanne
D. Werra: Ecole Polytechnique Fédérale de Lausanne

Journal of Combinatorial Optimization, 2005, vol. 10, issue 3, No 1, 225 pages

Abstract: 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.

Keywords: split-coloring; vertex covering by split graphs; partitioning; packing (search for similar items in EconPapers)
Date: 2005
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DOI: 10.1007/s10878-005-4103-7

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