Packing k-partite k-uniform hypergraphs

Let G and H be k-graphs (k-uniform hypergraphs); then a perfect H-packing in G is a collection of vertex-disjoint copies of H in G which together cover every vertex of G. For any fixed k-graph H let δ ( H , n ) be the minimum δ such that any k-graph G on n vertices with minimum codegree δ ( G ) ⩾ δ contains a perfect H-packing. The problem of determining δ ( H , n ) has been widely studied for graphs (i.e. 2-graphs), but little is known for k ⩾ 3 . Here we determine the asymptotic value of δ ( H , n ) for all complete k-partite k-graphs.