Hitting All Maximum Cliques with a Stable Set Using Lopsided Independent Transversals

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. (C) 2010 Wiley Periodicals, Inc. J Graph Theory 67: 300-305, 2011