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 colouring 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

Haxell, Penny

Peng, Y

Rodl, V

Rucinski, Andrzej

Skokan, Jozef

Łucak, T

LSE Research Online

English

3-uniform hypergraphs of bounded degree have linear Ramsey numbers.

A Dirac-type theorem for 3-uniform hypergraphs.

All Ramsey numbers for cycles in graphs.

B o n d y ,J .A .a n dE r d ˝ os, P.

Embeddings and Ramsey numbers of sparse k-uniform hypergraphs. Combinatorica,t oa p p e a r .

Extremal problems on set systems.

F i g a j ,A .a n d

L u c z a k ,T . ,P e n g ,Y .

Long monochromatic Berge cycles in colored 4-uniform hypergraphs.

Monochromatic Hamiltonian 3-tight Berge cycles in 2-colored 4-uniform hypergraphs.

On a Ramsey-type problem of

On the Ramsey number of sparse 3-graphs.

R(Cn,C n,C n)

Ramsey numbers of sparse hypergraphs. Random Struct. Algorithms,t oa p p e a r .

Regular partitions of graphs.

Short paths in quasi-random triple systems with sparse underlying graphs.

Small Ramsey numbers.

The Ramsey number of diamond-matchings and loose cycles in hypergraphs.

The Ramsey Number for 3-Uniform Tight Hypergraph Cycles