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The complexity of proving that a graph is Ramsey
KTH, School of Computer Science and Communication (CSC), Theoretical Computer Science, TCS.ORCID iD: 0000-0003-4003-3168
2013 (English)In: Automata, Languages, and Programming: 40th International Colloquium, ICALP 2013, Riga, Latvia, July 8-12, 2013, Proceedings, Part I, Springer, 2013, no PART 1, 684-695 p.Conference paper, Published paper (Refereed)
Abstract [en]

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 Ramsey graph must contain a large subgraph with some of the statistical properties of the random graph.

Place, publisher, year, edition, pages
Springer, 2013. no PART 1, 684-695 p.
Series
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), ISSN 0302-9743 ; 7965 LNCS
Keyword [en]
CNF formulas, Independent set, Lower bounds, Random graphs, Resolution proofs, Statistical properties, Subgraphs, Automata theory, Graph theory
National Category
Computer Science
Identifiers
URN: urn:nbn:se:kth:diva-134079DOI: 10.1007/978-3-642-39206-1_58ISI: 000342686600058Scopus ID: 2-s2.0-84880262321ISBN: 978-364239205-4 (print)OAI: oai:DiVA.org:kth-134079DiVA: diva2:664560
Conference
40th International Colloquium on Automata, Languages, and Programming, ICALP 2013; Riga; Latvia; 8 July 2013 through 12 July 2013
Note

QC 20131115

Available from: 2013-11-15 Created: 2013-11-15 Last updated: 2014-11-07Bibliographically approved

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Lauria, Massimo

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CiteExportLink to record
Permanent link

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Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
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  • asciidoc
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