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Combinatorica

, Volume 37, Issue 2, pp 253–268 | Cite as

The complexity of proving that a graph is Ramsey

  • Massimo Lauria
  • Pavel Pudlák
  • Vojtěch Rödl
  • Neil Thapen
Original Paper

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.

Mathematics Subject Classification (2000)

03F20 05C55 

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Copyright information

© János Bolyai Mathematical Society and Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

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

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