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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.

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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