The complexity of proving that a graph is ramsey

Authors:
Massimo Lauria;Pavel Pudlák;Vojtěch Rödl;Neil Thapen
Affiliations:
Royal Institute of Technology, Stockholm, Sweden;Academy of Sciences of the Czech Republic, Czech Republic;Emory University, Atlanta;Academy of Sciences of the Czech Republic, Czech Republic
Venue:
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
Year:
2013

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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 logn. 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.