The Ramsey number of loose triangles and quadrangles in hypergraphs

A. Gyárfás, Ghaffar Raeisi

Research output: Article

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 - jún. 6 2012

Fingerprint

Ramsey number
Hypergraph
Triangle
Color
Cycle
Path
Graph in graph theory

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: Article

@article{7f24e71026b04a3a924a8624f3105953,
title = "The Ramsey number of loose triangles and quadrangles in hypergraphs",
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.",
keywords = "Hypergraph ramsey number, Loose cycle, Loose path",
author = "A. Gy{\'a}rf{\'a}s and Ghaffar Raeisi",
year = "2012",
month = "6",
day = "6",
language = "English",
volume = "19",
pages = "1--9",
journal = "Electronic Journal of Combinatorics",
issn = "1077-8926",
publisher = "Electronic Journal of Combinatorics",
number = "2",

}

TY - JOUR

T1 - The Ramsey number of loose triangles and quadrangles in hypergraphs

AU - Gyárfás, A.

AU - Raeisi, Ghaffar

PY - 2012/6/6

Y1 - 2012/6/6

N2 - 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.

AB - 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.

KW - Hypergraph ramsey number

KW - Loose cycle

KW - Loose path

UR - http://www.scopus.com/inward/record.url?scp=84863498997&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84863498997&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84863498997

VL - 19

SP - 1

EP - 9

JO - Electronic Journal of Combinatorics

JF - Electronic Journal of Combinatorics

SN - 1077-8926

IS - 2

ER -