Integer and fractional packings of hypergraphs (Q864903)

Let \(F_0\) be a \(k\)-uniform hypergraph. The problem of finding the integer \(F_0\)-packing number \(\nu_{F_0}(\mathcal H)\) of a \(k\)-uniform hypergraph \(\mathcal H\) is NP-hard. Finding the fractional \(F_0\)-packing number \(\nu^*_{F_0}(\mathcal H)\) however can be done in polynomial time. The authors present a lower bound for \(\nu_{F_0}(\mathcal H)\) in terms of \(\nu^*_{F_0}(\mathcal H)\), and they prove that \(\nu_{F_0}(\mathcal H)\geq\nu^*_{F_0}(\mathcal H)- o(| V(\mathcal H)| ^k),\) where \(V(\mathcal H)\) is the vertex set of the \(k\)-uniform hypergraph \(\mathcal H\).