Packing of partial designs

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Abstract

We say that two hypergraphs H1 and H2 with v vertices each can be packed if there are edge disjoint hypergraphs H1and H2on the same set V of v vertices, where Hiis isomorphic to Hi.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 (λ1, t,k,v) partial design and a (λ1, t,k,v) partial design that cannot be packed, where λ1 λ2≤O(vk-2t+1log v). Both results are nearly optimal asymptotically and answer questions of Teirlinck. The proofs are probabilistic.

Original languageEnglish (US)
Pages (from-to)11-18
Number of pages8
JournalGraphs and Combinatorics
Volume10
Issue number1
DOIs
StatePublished - Mar 1 1994
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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