  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.
