# 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 language English 1-9 9 Electronic Journal of Combinatorics 19 2 Published - Jun 6 2012

### Fingerprint

Ramsey number
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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

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

Research output: Contribution to journalArticle

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