The Ramsey Number for 3-Uniform Tight Hypergraph Cycles
2009; Cambridge University Press; Volume: 18; Issue: 1-2 Linguagem: Inglês
10.1017/s096354830800967x
ISSN1469-2163
AutoresPenny Haxell, Tomasz Łuczak, Yuejian Peng, V. Rödl, Andrzej Ruciński, Jozef Skokan,
Tópico(s)Advanced Graph Theory Research
ResumoLet C (3) n denote the 3-uniform tight cycle , that is, the hypergraph with vertices v 1 , .–.–., v n and edges v 1 v 2 v 3 , v 2 v 3 v 4 , .–.–., v n −1 v n v 1 , v n v 1 v 2 . 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 4 n /3 if n is divisible by 3, and 2 n otherwise. The proof uses the regularity lemma for hypergraphs of Frankl and Rödl.
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