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A Note on Hitting Maximum and Maximal Cliques With a Stable Set

Authors


  • Supported by (FP7/2007-2013)/ERC grant agreement no. 259385. Supported by an NSERC PGS Fellowship and a Gordon Wu Scholarship. Supported by an EBCO/Ebbich Postdoctoral Scholarship and the NSERC Discovery Grants of Pavol Hell and Bojan Mohar.

Abstract

It was recently proved that any graph satisfying math formula contains a stable set hitting every maximum clique. In this note, we prove that the same is true for graphs satisfying math formula unless the graph is the strong product of an odd hole and math formula.We also provide a counterexample to a recent conjecture on the existence of a stable set hitting every sufficiently large maximal clique.

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