The complexity of proving that a graph is Ramsey

Massimo Lauria; Pavel Pudlák; Vojtěch Rödl; Neil Thapen

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arXiv · 1303.3166

The complexity of proving that a graph is Ramsey

Massimo Lauria·Pavel Pudlák·Vojtěch Rödl·Neil Thapen

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Abstract

We say that a graph with $n$ vertices is $c$-Ramsey if it does not contain either a clique or an independent set of size $c \log n$. We define a CNF formula which expresses this property for a graph $G$. We show a superpolynomial lower bound on the length of resolution proofs that $G$ is $c$-Ramsey, for every graph $G$. Our proof makes use of the fact that every Ramsey graph must contain a large subgraph with some of the statistical properties of the random graph.

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Massimo Lauria, Pavel Pudlák, Vojtěch Rödl, Neil Thapen. 2013-03-13. The complexity of proving that a graph is Ramsey. https://arxiv.org/abs/1303.3166

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