Abstract
A clique-transversal set D of a graph G is a set of vertices of G such that D meets all cliques of G. The clique-transversal number, denoted τc(G), is the minimum cardinality of a clique-transversal set in G. In this paper we present the bounds on the clique-transversal number for regular graphs and characterize the extremal graphs achieving the lower bound. Also, we give the sharp bounds on the clique-transversal number for claw-free cubic graphs and we characterize the extremal graphs achieving the lower bound.
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