Enumerating the maximal cliques of a circle graph

Abstract

We describe the notion of locally transitive orientations of an undirected graph, as a generalization of ordinarytransitive orientations. As an application, we obtain an algorithm for generating all maximal cliquesof a circle graph G in time 0(n(m+α)), where n,m and a are the number of vertices, edges and maximal cliques of G. In addition, we show that the actual number of such cliques can be computedin 0(nm) time.