The Ramsey number of loose triangles and quadrangles in hypergraphs

A. Gyárfás, Ghaffar Raeisi

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

Asymptotic values of hypergraph Ramsey numbers for loose cycles (and paths) were determined recently. Here we determine some of them exactly, for example the 2-color hypergraph Ramsey number of a k-uniform loose 3-cycle or 4-cycle:R(C k 3,C k 3)=3k-2 and R(C k 4, C k 4) = 4k-3 (for k≥3). For more than 3 colors we could [prove only that R (C 3 3, C 3 3, C 3 3) = 8. Nevertheless, the r-color Ramsey number of triangles for hypergraphs are much smaller than for graphs: for r≥3, r+5≤R(C 3 3, C 3 3,... C 3 3)≤3r.

Original languageEnglish
Pages (from-to)1-9
Number of pages9
JournalElectronic Journal of Combinatorics
Volume19
Issue number2
Publication statusPublished - Jun 6 2012

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Keywords

  • Hypergraph ramsey number
  • Loose cycle
  • Loose path

ASJC Scopus subject areas

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

Cite this

The Ramsey number of loose triangles and quadrangles in hypergraphs. / Gyárfás, A.; Raeisi, Ghaffar.

In: Electronic Journal of Combinatorics, Vol. 19, No. 2, 06.06.2012, p. 1-9.

Research output: Contribution to journalArticle

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