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The Ramsey number for hypergraph cycles I

2005; Elsevier BV; Volume: 113; Issue: 1 Linguagem: Inglês

10.1016/j.jcta.2005.02.005

1096-0899

Penny Haxell, Tomasz Łuczak, Yuejian Peng, V. Rödl, Andrzej Ruciński, Miklós Simonovits, Jozef Skokan,

Advanced Graph Theory Research

Let Cn denote the 3-uniform hypergraph loose cycle, that is the hypergraph with vertices v1,…,vn and edges v1v2v3, v3v4v5, v5v6v7,…,vn-1vnv1. We prove that every red-blue colouring of the edges of the complete 3-uniform hypergraph with N vertices contains a monochromatic copy of Cn, where N is asymptotically equal to 5n/4. Moreover this result is (asymptotically) best possible.