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 c-Ramsey graph must contain a large subgraph with some properties typical for random graphs.
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Lauria, M., Pudlák, P., Rödl, V. et al. The complexity of proving that a graph is Ramsey. Combinatorica 37, 253–268 (2017). https://doi.org/10.1007/s00493-015-3193-9
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DOI: https://doi.org/10.1007/s00493-015-3193-9