Journal of Combinatorial Optimization

, Volume 10, Issue 3, pp 211–225 | Cite as

On Split-Coloring Problems

  • T. Ekim
  • D. de Werra


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.


split-coloring vertex covering by split graphs partitioning packing 


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Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Institute of Mathematics—ROSEEcole Polytechnique Fédérale de LausanneLausanne-EcublensSwitzerland

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