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The Ramsey number for hypergraph cycles II

Haxell, Penny, Luczak, Tomasz, Peng, Yuejian, Rodl, V, Rucinski, Andrzej and Skokan, Jozef (2007) The Ramsey number for hypergraph cycles II. LSE-CDAM-2007-04. London School of Economics and Political Science, London, UK.

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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 coloring 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: Monograph (Report)
Official URL: http://www.cdam.lse.ac.uk/Reports/
Additional Information: © 2007 London school of economics and political science
Library of Congress subject classification: H Social Sciences > H Social Sciences (General)
Sets: Departments > Mathematics
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Identification Number: LSE-CDAM-2007-04
Date Deposited: 11 Jul 2008 11:44
URL: http://eprints.lse.ac.uk/6907/

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