On the approximation of Min Split-coloring and Min Cocoloring

Abstract

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 [,,]. Also, we provide some results on the approximability of Min Cocoloring and comparisons with Min Split-coloring and Min Coloring.