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On covering all cliques of a chordal graph. (English) Zbl 0846.05050
Let $$G$$ be a graph without isolated vertices. A set $$T\subseteq V(G)$$ is called a clique-transversal set if $$T$$ has non-empty intersection with every maximal clique in $$G$$. The clique-transversal number $$\tau_c(G)$$ is the minimum cardinality of a clique-transversal set. Let $$\mathcal G$$ denote the class of chordal graphs with the property that each edge is contained in a clique of order at least 4. The authors show that for each $$\varepsilon> 0$$, there exists a graph $$G\in {\mathcal G}$$ such that $$\tau_c(G)\geq ({2\over 7}- \varepsilon)$$. They give some evidence to support their conjecture that $$\tau_c(G)\leq {2\over 7} |V(G)|$$ for all $$G\in {\mathcal G}$$.

##### MSC:
 05C35 Extremal problems in graph theory 05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
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##### References:
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