Hitting all maximum cliques with a stable set using lopsided independent transversals



Rabern recently proved that any graph with equation image contains a stable set meeting all maximum cliques. We strengthen this result, proving that such a stable set exists for any graph with equation image. 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. © 2010 Wiley Periodicals, Inc. J Graph Theory 67:300-305, 2011