### Abstract

Let f (n, r) be the largest integer m with the following property: if the edges of the complete 3-uniform hypergraph K_{n}^{3} are colored with r colors then there is a monochromatic component with at least m vertices. Here we show that f (n, 5) ≥ frac(5 n, 7) and f (n, 6) ≥ frac(2 n, 3). Both results are sharp under suitable divisibility conditions (namely if n is divisible by 7, or by 6 respectively).

Original language | English |
---|---|

Pages (from-to) | 3156-3160 |

Number of pages | 5 |

Journal | Discrete Mathematics |

Volume | 309 |

Issue number | 10 |

DOIs | |

Publication status | Published - May 28 2009 |

### Fingerprint

### Keywords

- Hypergraph edge coloring
- Monochromatic components

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Discrete Mathematics*,

*309*(10), 3156-3160. https://doi.org/10.1016/j.disc.2008.09.004

**Large monochromatic components in colorings of complete 3-uniform hypergraphs.** / Gyárfás, A.; Haxell, Penny.

Research output: Contribution to journal › Article

*Discrete Mathematics*, vol. 309, no. 10, pp. 3156-3160. https://doi.org/10.1016/j.disc.2008.09.004

}

TY - JOUR

T1 - Large monochromatic components in colorings of complete 3-uniform hypergraphs

AU - Gyárfás, A.

AU - Haxell, Penny

PY - 2009/5/28

Y1 - 2009/5/28

N2 - Let f (n, r) be the largest integer m with the following property: if the edges of the complete 3-uniform hypergraph Kn3 are colored with r colors then there is a monochromatic component with at least m vertices. Here we show that f (n, 5) ≥ frac(5 n, 7) and f (n, 6) ≥ frac(2 n, 3). Both results are sharp under suitable divisibility conditions (namely if n is divisible by 7, or by 6 respectively).

AB - Let f (n, r) be the largest integer m with the following property: if the edges of the complete 3-uniform hypergraph Kn3 are colored with r colors then there is a monochromatic component with at least m vertices. Here we show that f (n, 5) ≥ frac(5 n, 7) and f (n, 6) ≥ frac(2 n, 3). Both results are sharp under suitable divisibility conditions (namely if n is divisible by 7, or by 6 respectively).

KW - Hypergraph edge coloring

KW - Monochromatic components

UR - http://www.scopus.com/inward/record.url?scp=67349136772&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=67349136772&partnerID=8YFLogxK

U2 - 10.1016/j.disc.2008.09.004

DO - 10.1016/j.disc.2008.09.004

M3 - Article

AN - SCOPUS:67349136772

VL - 309

SP - 3156

EP - 3160

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 10

ER -