### 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 |
---|---|

Pages (from-to) | 1-9 |

Number of pages | 9 |

Journal | Electronic Journal of Combinatorics |

Volume | 19 |

Issue number | 2 |

Publication status | Published - 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

*Electronic Journal of Combinatorics*,

*19*(2), 1-9.

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

Research output: Contribution to journal › Article

*Electronic Journal of Combinatorics*, vol. 19, no. 2, pp. 1-9.

}

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 -