Approximating minimum cocolourings

Abstract

A cocolouring of a graph G is a partition of the vertex set of G such that each set of the partition is either a clique or an independent set in G. So0me special cases of the minimum cocolouring problem are of particular interest. We provide polynomial-time algorithms to approximate a mimimum cocolouring on graphs, partially ordered sets and sequences. In particular, we obtain an efficient algorithm to approximate within a factor of 1.71 a minimum partition of a partially ordered set into chains and antichains, and a minimum partition of a sequence into increasing and decreasing subsequences.