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The Ramsey Number for 3-Uniform Tight Hypergraph Cycles

Haxell, Penny, Łucak, T, Peng, Y, Rodl, V, Rucinski, Andrzej and Skokan, Jozef (2009) The Ramsey Number for 3-Uniform Tight Hypergraph Cycles. Combinatorics, Probability and Computing, 18 (1-2). pp. 165-203. ISSN 0963-5483

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Abstract

Let C(3)n denote the 3-uniform tight cycle, that is, the hypergraph with vertices v1, .–.–., vn and edges v1v2v3, v2v3v4, .–.–., vn−1vnv1, vnv1v2. We prove that the smallest integer N = N(n) for which every red–blue colouring of the edges of the complete 3-uniform hypergraph with N vertices contains a monochromatic copy of C(3)n is asymptotically equal to 4n/3 if n is divisible by 3, and 2n otherwise. The proof uses the regularity lemma for hypergraphs of Frankl and Rödl.

Item Type: Article
Official URL: http://journals.cambridge.org/action/displayJourna...
Additional Information: © 2009 Cambridge University Press
Library of Congress subject classification: Q Science > QA Mathematics
Sets: Departments > Mathematics
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Date Deposited: 27 Apr 2009 12:07
URL: http://eprints.lse.ac.uk/23751/

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