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The Ramsey Number for 3-Uniform Tight Hypergraph Cycles

  • P. E. HAXELL (a1), T. ŁUCZAK (a2), Y. PENG (a3), V. RÖDL (a4), A. RUCIŃSKI (a2) and J. SKOKAN (a5)...

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.

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[1]J. A. Bondy and P. Erdős (1973) Ramsey numbers for cycles in graphs. J. Combin. Theory Ser. B 14 4654.

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[18]V. Rosta (1973) On a Ramsey-type problem of J. A. Bondy and P. Erdős, I and II. J. Combin. Theory Ser. B 15 94104, 105–120.

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Combinatorics, Probability and Computing
  • ISSN: 0963-5483
  • EISSN: 1469-2163
  • URL: /core/journals/combinatorics-probability-and-computing
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