The Ramsey number for hypergraph cycles I

Authors:
P. E. Haxell;T. Łuczak;Y. Peng;V. Rödl;A. Ruciński;M. Simonovits;J. Skokan
Affiliations:
Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada;Department of Discrete Mathematics, Adam Mickiewicz University, Poznań, Poland;Department of Mathematics and Computer Science, Indiana State University, Terre Haute, IN;Department of Mathematics and Computer Science, Emory University, Atlanta, GA;Department of Discrete Mathematics, Adam Mickiewicz University, Poznań, Poland;Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, Reáltanoda u.;Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL and Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão, São P ...
Venue:
Journal of Combinatorial Theory Series A
Year:
2006

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Abstract

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.