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arXiv · 1109.3092

A note on hitting maximum and maximal cliques with a stable set

Demetres Christofides·Katherine Edwards·Andrew D. King
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Abstract

It was recently proved that any graph satisfying $ω> \frac 23(Δ+1)$ contains a stable set hitting every maximum clique. In this note we prove that the same is true for graphs satisfying $ω\geq \frac 23(Δ+1)$ unless the graph is the strong product of $K_{ω/2}$ and an odd hole. 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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Demetres Christofides, Katherine Edwards, Andrew D. King. 2012-05-28. A note on hitting maximum and maximal cliques with a stable set. https://arxiv.org/abs/1109.3092

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