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The Ramsey number for hypergraph cycles I |
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| Authors: | P.E. Haxell |
| Affiliation: | a Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1 b Department of Discrete Mathematics, Adam Mickiewicz University, 61-614 Poznań, Poland c Department of Mathematics and Computer Science, Indiana State University, Terre Haute, IN 47809, USA d Department of Mathematics and Computer Science, Emory University, Atlanta, GA 30032, USA e Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, H-1053 Budapest, Reáltanoda u. 13-15. f Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W. Green Street, Urbana, IL 61801, USA g Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão 1010, 05508-009 São Paulo, Brazil |
| 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. |
| Keywords: | Ramsey number Hypergraph Colouring Regularity lemma Cycle |
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