The clique-transversal set problem in {claw,K4}-free planar graphs

A clique is defined as a complete subgraph maximal under inclusion and having at least two vertices. A clique-transversal set D of a graph G=(V,E) is a subset of vertices of G such that D meets all cliques of G. The clique-transversal set problem is to find a minimum clique-transversal set of G. The clique-transversal set problem has been proved to be NP-complete in planar graphs. This paper gives a polynomial-time algorithm for the clique-transversal set problem in {claw,K4}-free planar graphs.