Claw-free cubic graphs with clique-transversal number half of their order

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 by τ C ( G ) , is the minimum cardinality of a clique-transversal set in G . In 2008, we showed that the clique-transversal number of every claw-free cubic graph is bounded above by half of its order. In this note we characterize claw-free cubic graphs which attain the upper bound.