### 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 |
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Pages (from-to) | 3156-3160 |

Number of pages | 5 |

Journal | Discrete Mathematics |

Volume | 309 |

Issue number | 10 |

DOIs | |

Publication status | Published - May 28 2009 |

### Keywords

- Hypergraph edge coloring
- Monochromatic components

### ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics

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## Cite this

Gyárfás, A., & Haxell, P. (2009). Large monochromatic components in colorings of complete 3-uniform hypergraphs.

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