### Abstract

If the edge sets of some r-uniform hypergraphs H_{1}, ..., H_{t} contain all the r-tuples of an n-element set, and each H_{i} has chromatic number at most k, then for the sum of the orders of the H_{i} we have Σ|V(H_{i})| ≥ (n log ( n (r - 1))) log k. In particular, if K_{n} ^{r} has an edge coloring such that each vertex is incident to edges of at most s colors and every monochromatic class of edges forms a k-vertex-colorable hypergraph, then n ≤ (r - 1) k^{s}. Both bounds are sharp.

Original language | English |
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Pages (from-to) | 79-85 |

Number of pages | 7 |

Journal | Journal of Combinatorial Theory, Series B |

Volume | 52 |

Issue number | 1 |

DOIs | |

Publication status | Published - May 1991 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics

## Fingerprint Dive into the research topics of 'Hypergraph coverings and local colorings'. Together they form a unique fingerprint.

## Cite this

Caro, Y., & Tuza, Z. (1991). Hypergraph coverings and local colorings.

*Journal of Combinatorial Theory, Series B*,*52*(1), 79-85. https://doi.org/10.1016/0095-8956(91)90092-X