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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
2017 (English)In: Combinatorica, ISSN 0209-9683, E-ISSN 1439-6912, Vol. 37, no 2, 253-268 p.Article in journal (Refereed) Published
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 c-Ramsey graph must contain a large subgraph with some properties typical for random graphs.

Place, publisher, year, edition, pages
SPRINGER HEIDELBERG , 2017. Vol. 37, no 2, 253-268 p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-207698DOI: 10.1007/s00493-015-3193-9ISI: 000399890000008ScopusID: 2-s2.0-85018519537OAI: oai:DiVA.org:kth-207698DiVA: diva2:1103798
Note

QC 20170531

Available from: 2017-05-31 Created: 2017-05-31 Last updated: 2017-05-31Bibliographically approved

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