Centre for Discrete and Applicable Mathematics 

CDAM Research Report, LSECDAM200704March 2007 
The Ramsey Number for Hypergraph Cycles II
P.E. Haxell, T. Luczak, Y. Peng, V. Rödl, A. Rucinski, and J. Skokan
Let C^{(3)}_{n} denote the 3uniform 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_{n1}v_{n}v_{1}, v_{n}v_{1}v_{2}. We prove that the smallest integer N = N(n) for which every redblue coloring 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.A PDF file (438 kB) with the full contents of this report can be downloaded by clicking here.
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