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)


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.


Random Graph Conjunctive Normal Form Propositional Variable Resolution Proof Proof Complexity 
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© 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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