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The Complexity of Proving That a Graph Is Ramsey

  • Massimo Lauria
  • Pavel Pudlák
  • Vojtěch Rödl
  • Neil Thapen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7965)

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.

Keywords

Random Graph Conjunctive Normal Form Propositional Variable Resolution Proof Proof Complexity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Massimo Lauria
    • 1
  • Pavel Pudlák
    • 2
  • Vojtěch Rödl
    • 3
  • Neil Thapen
    • 2
  1. 1.Royal Institute of TechnologyStockholmSweden
  2. 2.Academy of Sciences of the Czech RepublicCzech Republic
  3. 3.Emory UniversityAtlantaUSA

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