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The Ramsey number for hypergraph cycles II

By Penny Haxell, Tomasz Luczak, Yuejian Peng, V Rodl, Andrzej Rucinski and Jozef Skokan

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

Topics: H Social Sciences (General)
Publisher: London School of Economics and Political Science
Year: 2007
OAI identifier: oai:eprints.lse.ac.uk:6907
Provided by: LSE Research Online
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