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The Ramsey Number for 3-Uniform Tight Hypergraph Cycles

Haxell, Penny and Łucak, T and Peng, Y and Rodl, V and 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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Identification Number: 10.1017/S096354830800967X

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
Subjects: Q Science > QA Mathematics
Sets: Departments > Mathematics
Date Deposited: 27 Apr 2009 12:07
Last Modified: 13 Mar 2014 17:00
URI: http://eprints.lse.ac.uk/id/eprint/23751

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