EDGE-COLORING OF COMPLETE HYPERGRAPHS .1.

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-1n-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 Knh is 1-factorizable. In this paper we study the factorization and edge-coloring problems of the hypergraph Krxmh (which is the complete, regular, h-uniform, r-partite hypergraph with m vertices in each of the r classes of vertices). © 1979.