DMGT

A NOTE ON PACKING OF TWO COPIES OF A HYPERGRAPH

Monika Pilśniak

Faculty of Applied Mathematics
AGH University of Science and Technology
Mickiewicza 30, 30-059 Kraków, Poland
e-mail: pilsniak@agh.edu.pl

Mariusz Woźniak

Institute of Mathematics
Polish Academy of Sciences
Św. Tomasza 30, Kraków, Poland
e-mail: mwozniak@agh.edu.pl

A 2-packing of a hypergraph H is a permutation σ on V(H) such that if an edge e belongs to E(H), then σ (e) does not belong to E(H).

We prove that a hypergraph which does not contain neither empty edge ∅ nor complete edge V(H) and has at most [1/2]n edges is 2-packable.

A 1-uniform hypergraph of order n with more than [1/2]n edges shows that this result cannot be improved by increasing the size of H.

Keywords: packing, hypergraphs.

2000 Mathematics Subject Classification: 05C65, 05C70.

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Received 5 September 2005
Revised 12 January 2007