Publication details

Optimal-size clique transversals in chordal graphs


COOPER Jacob GRZESIK Andrzej KRÁĽ Daniel

Year of publication 2018
Type Article in Periodical
Magazine / Source Journal of Graph Theory
Keywords chordal graphs; clique transversals
Description 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.