### Abstract

Edge colorings of r-uniform hypergraphs naturally define a multicoloring on the 2-shadow, i.e., on the pairs that are covered by hyperedges. We show that in any (r - 1)-coloring of the edges of an r-uniform hypergraph with n vertices and at least edges, the 2-shadow has a monochromatic matching covering all but at most o(n) vertices. This result confirms an earlier conjecture and implies that for any fixed r and sufficiently large n, there is a monochromatic Berge-cycle of length (1 - o(1))n in every (r - 1)-coloring of the edges of K_{n}^{(r)}, the complete r-uniform hypergraph on n vertices.

Original language | English |
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Pages (from-to) | 245-249 |

Number of pages | 5 |

Journal | Annals of Combinatorics |

Volume | 14 |

Issue number | 2 |

DOIs | |

Publication status | Published - Jun 2010 |

### Keywords

- Colored complete uniform hypergraphs
- Monochromatic matchings

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics

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## Cite this

Gyárfás, A., Sárközy, G. N., & Szemerédi, E. (2010). Monochromatic matchings in the shadow graph of almost complete hypergraphs.

*Annals of Combinatorics*,*14*(2), 245-249. https://doi.org/10.1007/s00026-010-0058-1