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The Complexity of Proving That a Graph Is Ramsey

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Automata, Languages, and Programming (ICALP 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7965))

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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.

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Author information

Authors and Affiliations

  1. Royal Institute of Technology, Sweden, Stockholm

    Massimo Lauria

  2. Academy of Sciences of the Czech Republic, Czech Republic

    Pavel Pudlák & Neil Thapen

  3. Emory University, Atlanta, USA

    Vojtěch Rödl

Authors
  1. Massimo Lauria
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  2. Pavel Pudlák
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  3. Vojtěch Rödl
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  4. Neil Thapen
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Editor information

Editors and Affiliations

  1. Department of Informatics, University of Bergen, Postboks 7803, 5020, Bergen, Norway

    Fedor V. Fomin

  2. Faculty of Computing, University of Latvia, Raina bulv. 19, 1586, Riga, Latvia

    Rūsiņš Freivalds

  3. Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, OX1 3QD, Oxford, UK

    Marta Kwiatkowska

  4. Faculty of Mathematics and Computer Science, Weizmann Institute of Science, POB 26, 76100, Rehovot, Israel

    David Peleg

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Lauria, M., Pudlák, P., Rödl, V., Thapen, N. (2013). The Complexity of Proving That a Graph Is Ramsey. In: Fomin, F.V., Freivalds, R., Kwiatkowska, M., Peleg, D. (eds) Automata, Languages, and Programming. ICALP 2013. Lecture Notes in Computer Science, vol 7965. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39206-1_58

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  • DOI: https://doi.org/10.1007/978-3-642-39206-1_58

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-39205-4

  • Online ISBN: 978-3-642-39206-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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