### Abstract

Let H = (V, E) be an r-uniform hypergraph and let ℱ ⊂ 2 ^{V}. A matching M of H is (α, ℱ)-perfect if for each ℱ ∈ ℱ, at least α F| vertices of F are covered by M. Our main result is a theorem giving sufficient conditions for an r-uniform hypergraph to have a (1 - ε, ℱ-perfect matching. As a special case of our theorem we obtain the following result. Let K(n, r) denote the complete r-uniform hypergraph with n vertices. Let t and r be fixed positive integers where t ≥ r ≥ 2. Then, K (n, r) can be packed with edge-disjoint copies of K(t, r) such that each vertex is incident with only o(n^{r-1}) unpacked edges. This extends a result of Rödl [9].

Original language | English (US) |
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Pages (from-to) | 377-384 |

Number of pages | 8 |

Journal | Graphs and Combinatorics |

Volume | 21 |

Issue number | 4 |

DOIs | |

State | Published - Dec 1 2005 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics

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## Cite this

Alon, N., & Yuster, R. (2005). On a hypergraph matching problem.

*Graphs and Combinatorics*,*21*(4), 377-384. https://doi.org/10.1007/s00373-005-0628-x