### Abstract

We say that two hypergraphs H_{1} and H_{2} with v vertices each can be packed if there are edge disjoint hypergraphs H_{1}^{′}and H_{2}^{′}on the same set V of v vertices, where H_{i}^{′}is isomorphic to H_{i}.It is shown that for every fixed integers k and t, where t≤k≤2t-2 and for all sufficiently large v there are two (t, k, v) partial designs that cannot be packed. Moreover, there are two isomorphic partial (t, k, v)-designs that cannot be packed. It is also shown that for every fixed k≥2t-1 and for all sufficiently large v there is a (λ_{1}, t,k,v) partial design and a (λ_{1}, t,k,v) partial design that cannot be packed, where λ_{1} λ_{2}≤O(v^{k-2t+1}log v). Both results are nearly optimal asymptotically and answer questions of Teirlinck. The proofs are probabilistic.

Original language | English (US) |
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Pages (from-to) | 11-18 |

Number of pages | 8 |

Journal | Graphs and Combinatorics |

Volume | 10 |

Issue number | 1 |

DOIs | |

State | Published - Mar 1 1994 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics

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## Cite this

*Graphs and Combinatorics*,

*10*(1), 11-18. https://doi.org/10.1007/BF01202465