Optimal-size clique transversals in chordal graphs
Combinatorics
2018-04-05 v2
Abstract
The following question was raised by Tuza in 1990 and Erdos 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 non-trivial 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.
Keywords
Cite
@article{arxiv.1601.05305,
title = {Optimal-size clique transversals in chordal graphs},
author = {Jacob W. Cooper and Andrzej Grzesik and Daniel Kral},
journal= {arXiv preprint arXiv:1601.05305},
year = {2018}
}