A note on hitting maximum and maximal cliques with a stable set
نویسندگان
چکیده
It was recently proved that any graph satisfying ω > 2 3(∆ + 1) contains a stable set hitting every maximum clique. In this note we prove that the same is true for graphs satisfying ω ≥ 23(∆ + 1) unless the graph is the strong product of an odd hole and Kω/2. We also provide a counterexample to a recent conjecture on the existence of a stable set hitting every sufficiently large maximal clique.
منابع مشابه
Hitting all maximum cliques with a stable set using lopsided independent transversals
Rabern recently proved that any graph with ω ≥ 3 4(∆+1) contains a stable set meeting all maximum cliques. We strengthen this result, proving that such a stable set exists for any graph with ω > 23(∆ + 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.
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ورودعنوان ژورنال:
- Journal of Graph Theory
دوره 73 شماره
صفحات -
تاریخ انتشار 2013