Haxell, Penny, Łucak, T, Peng, Y, Rodl, V, Rucinski, Andrzej and Skokan, Jozef
(2009)
The Ramsey Number for 3Uniform Tight Hypergraph Cycles.
Combinatorics, Probability and Computing, 18 (12).
pp. 165203.
ISSN 09635483
Abstract
Let C(3)n denote the 3uniform 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 colouring of the edges of the complete 3uniform 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.
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