On the approximation of Min Split-coloring and Min Cocoloring

We consider two problems, namely Min Split-coloring and Min Cocoloring, that generalize the classical Min Coloring problem by using not only stable sets but also cliques to cover all the vertices of a given graph. We prove the NP-hardness of some cases. We derive approximation results for Min Split-coloring and Min Cocoloring in line graphs, comparability graphs and general graphs. This provides to our knowledge the first approximation results for Min Split-coloring since it was defined only very recently [8, 9, 13]. Also, we provide some results on the approximability of Min Cocoloring and comparisons with Min Split-coloring and Min Coloring. Article Type Communicated by Submitted Revised regular paper M. Fürer June 2005 April 2006 The research of Tınaz Ekim was supported by Grant 200021-101455/1 of the Swiss National Science Foundation whose support is greatly acknowledged. M. Demange et al., Min Split-coloring , JGAA, 10(2) 297–315 (2006) 298