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

A. Gyárfás, Gábor N. Sárkózyy, E. Szemerédi

Research output: Contribution to journalArticle

18 Citations (Scopus)

Abstract

The 2-color Ramsey number R(Cn3, Cn 3) of a 3-uniform loose cycle Cn is asymptotic to 5n/4 as has been recently proved by Haxell, Łuczak, Peng, Rödl, Ruciński, Simonovits and Skokan. Here we extend their result to the r-uniform case by showing that the corresponding Ramsey number is asymptotic to (2r-1)n/2r-2. Partly as a tool, partly as a subject of its own, we also prove that for r ≥ 2, R(kDr, kDr) = k(2r - 1) -1 and R(kDr, kDr, kDr) = 2kr - 2 where kDr is the hypergraph having k disjoint copies of two r-element hyperedges intersecting in two vertices.

Original languageEnglish
Article numberR126
JournalElectronic Journal of Combinatorics
Volume15
Issue number1 R
Publication statusPublished - Oct 13 2008

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Ramsey number
Strombus or kite or diamond
Hypergraph
Diamonds
Color
Cycle
Disjoint

ASJC Scopus subject areas

  • Geometry and Topology
  • Theoretical Computer Science
  • Computational Theory and Mathematics

Cite this

The Ramsey number of diamond-matchings and loose cycles in hypergraphs. / Gyárfás, A.; Sárkózyy, Gábor N.; Szemerédi, E.

In: Electronic Journal of Combinatorics, Vol. 15, No. 1 R, R126, 13.10.2008.

Research output: Contribution to journalArticle

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