Integer and fractional packings of hypergraphs

Let F 0 be a fixed k-uniform hypergraph. The problem of finding the integer F 0 -packing number ν F 0 ( H ) of a k-uniform hypergraph H is an NP-hard problem. Finding the fractional F 0 -packing number ν F 0 ∗ ( H ) however can be done in polynomial time. In this paper we give a lower bound for the integer F 0 -packing number ν F 0 ( H ) in terms of ν F 0 ∗ ( H ) and show that ν F 0 ( H ) ⩾ ν F 0 ∗ ( H ) − o ( | V ( H ) | k ) .