Algorithms on clique separable graphs

Algorithms for finding clique-transversals of graphs

A clique-transversal of a graph G is a subset of vertices intersecting all the cliques of G. It is NP-hard to determine the minimum cardinality τc of a clique-transversal of G. In this work, first we propose an algorithm for determining this parameter for a general graph, which runs in polynomial time, for fixed τc. This algorithm is employed for finding the minimum cardinality clique-transvers...

On hereditary clique-Helly self-clique graphs

A graph is clique-Helly if any family of mutually intersecting (maximal) cliques has non-empty intersection, and it is hereditary clique-Helly (abbreviated HCH) if its induced subgraphs are clique-Helly. The clique graph of a graph G is the intersection graph of its cliques, and G is self-clique if it is connected and isomorphic to its clique graph. We show that every HCH graph is an induced su...

On weighted clique graphs

Let K(G) be the clique graph of a graph G. A m-weighting of K(G) consists on giving to each m-size subset of its vertices a weight equal to the size of the intersection of the m corresponding cliques of G. The 2weighted clique graph was previously considered by McKee. In this work we obtain a characterization of weighted clique graphs similar to Roberts and Spencer’s characterization for clique...

On clique convergent graphs

A graph G is convergent when there is some nite integer n 0, such that the n-th iterated clique graph K n (G) has only one vertex. The smallest such n is the index of G. The Helly defect of a convergent graph is the smallest n such that K n (G) is clique Helly, that is, its maximal cliques satisfy the Helly property. Bandelt and Prisner proved that the Helly defect of a chordal graph is at most...

On clique-complete graphs