### 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 - 1991 |

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### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Journal of Combinatorial Theory. Series B*,

*52*(1), 79-85. https://doi.org/10.1016/0095-8956(91)90092-X

**Hypergraph coverings and local colorings.** / Caro, Yair; Tuza, Z.

Research output: Contribution to journal › Article

*Journal of Combinatorial Theory. Series B*, vol. 52, no. 1, pp. 79-85. https://doi.org/10.1016/0095-8956(91)90092-X

}

TY - JOUR

T1 - Hypergraph coverings and local colorings

AU - Caro, Yair

AU - Tuza, Z.

PY - 1991

Y1 - 1991

N2 - If the edge sets of some r-uniform hypergraphs H1, ..., Ht contain all the r-tuples of an n-element set, and each Hi has chromatic number at most k, then for the sum of the orders of the Hi we have Σ|V(Hi)| ≥ (n log ( n (r - 1))) log k. In particular, if Knr 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) ks. Both bounds are sharp.

AB - If the edge sets of some r-uniform hypergraphs H1, ..., Ht contain all the r-tuples of an n-element set, and each Hi has chromatic number at most k, then for the sum of the orders of the Hi we have Σ|V(Hi)| ≥ (n log ( n (r - 1))) log k. In particular, if Knr 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) ks. Both bounds are sharp.

UR - http://www.scopus.com/inward/record.url?scp=44949281902&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=44949281902&partnerID=8YFLogxK

U2 - 10.1016/0095-8956(91)90092-X

DO - 10.1016/0095-8956(91)90092-X

M3 - Article

AN - SCOPUS:44949281902

VL - 52

SP - 79

EP - 85

JO - Journal of Combinatorial Theory. Series B

JF - Journal of Combinatorial Theory. Series B

SN - 0095-8956

IS - 1

ER -