Hitting all maximum cliques with a stable set using lopsided independent transversals
Discrete Mathematics
2011-02-11 v4 Combinatorics
Abstract
Rabern recently proved that any graph with omega >= (3/4)(Delta+1) contains a stable set meeting all maximum cliques. We strengthen this result, proving that such a stable set exists for any graph with omega > (2/3)(Delta+1). This is tight, i.e. the inequality in the statement must be strict. The proof relies on finding an independent transversal in a graph partitioned into vertex sets of unequal size.
Cite
@article{arxiv.0911.1741,
title = {Hitting all maximum cliques with a stable set using lopsided independent transversals},
author = {Andrew D. King},
journal= {arXiv preprint arXiv:0911.1741},
year = {2011}
}
Comments
7 pages. v4: Correction to statement of Lemma 8 and clarified proof.