Optimal‐size clique transversals in chordal graphs.

The following question was raised by Tuza in 1990 and Erdős et al. in 1992: if every edge of an n‐vertex chordal graph G is contained in a clique of size at least four, does G have a clique transversal, i.e. a set of vertices meeting all nontrivial maximal cliques, of size at most n/4? We prove that every such graph G has a clique transversal of size at most 2(n−1)/7 if n≥5, which is the best possible bound. [ABSTRACT FROM AUTHOR]