Algorithms on clique separable graphs

Abstract We define a family of graphs, called the clique separable graphs , characterized by the fact that they have completely connected cut sets by which we decompose them into parts such that when no further decomposition is possible we have a set of simple subgraphs. For example the chordal graphs and the i -triangulated graphs are clique separable graphs. The purpose of this paper is to describe polynomial time algorithms for the recognition of the clique separable graphs and for finding them a minimum coloring and a maximum clique.