English

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}
}
R2 v1 2026-06-22T12:33:26.918Z