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. © 2013 Springer-Verlag.
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CITATION STYLE
Lauria, M., Pudlák, P., Rödl, V., & Thapen, N. (2013). The complexity of proving that a graph is Ramsey. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7965 LNCS, pp. 684–695). https://doi.org/10.1007/978-3-642-39206-1_58
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