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Bounds on the clique-transversal number of regular graphs. (English) Zbl 1168.05046
Summary: 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 $$\tau _c (G)$$, 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.

MSC:
 05C65 Hypergraphs 05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) 05C75 Structural characterization of families of graphs
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