While doing research I came unto the following problem:


Given a hypergraph H r-partite, r-uniform (a r-graph, each edge contains r vertices), k-regular (all vertices have regular degree) and n-balanced (each partition contain n vertices), does H contain a perfect matching (an independent set of edges that covers all vertices)?

In the literature I've found results by Aharoni, Haxell, Alon, Rödl and others, but none seem to contain these hypothesis over the graph. Any suggestions or pointers to literature would be greatly appreciated.