Abstract
This paper contains and generalizes the solution of the following classical problem: If h | n then the h-element subsets of an n-element set can be partitioned into ( h−1 n−1 ) classes so that every class contains n h disjoint h-element sets and every h-element set appears in exactly one class. A short formulation of this statement is: If h | n then the hypergraph K n h is 1-factorizable. In this paper we study the factorization and edge-coloring problems of the hypergraph K rxm h (which is the complete, regular, h-uniform, r-partite hypergraph with m vertices in each of the r classes of vertices).
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