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Packing of partial designs Bellcore, Morristown, NJ 07960, USA
 

Summary: Packing of partial designs
Noga Alon
Bellcore, Morristown, NJ 07960, USA
and Department of Mathematics
Raymond and Beverly Sackler Faculty of Exact Sciences
Tel Aviv University, Tel Aviv, Israel
Abstract
We say that two hypergraphs H1 and H2 with v vertices each can be packed if there are edge
disjoint hypergraphs H1 and H2 on the same set V of v vertices, where Hi is 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 (1, t, k, v) partial design and a (2, t, k, v)
partial design that cannot be packed, where 12 O(vk-2t+1
log v). Both results are nearly
optimal asymptotically and answer questions of Teirlinck. The proofs are probabilistic.
1 Introduction
Let H1 = (V1, E1) and H2 = (V2, E2) be two hypergraphs, where |V1| = |V2| = v. We say that
H1 and H2 can be packed if there are edge disjoint hypergraphs H1 and H2 on the same set of v
vertices, where Hi is isomorphic to Hi for i = 1, 2.

  

Source: Alon, Noga - School of Mathematical Sciences, Tel Aviv University

 

Collections: Mathematics