Fractional decompositions of dense hypergraphs

A seminal result of Rodl (the Rodl nibble) asserts that the edges of the complete r-uniform hypergraph K-n(r) can be packed, almost completely, with copies of K-k(r), where k is fixed. We prove that the same result holds in a dense hypergraph setting. It is shown that for every r-uniform hypergraph H-o, there exists a constant alpha = alpha(H-o) < 1 such that every r-uniform hypergraph H in which every (r - 1)-set is contained in at least alpha n edges has an H-o-packing that covers \E(H)\ (1 - o(n)(1)) edges. Our method of proof uses fractional decompositions and makes extensive use of probabilistic arguments and additional combinatorial ideas.