ON A PROBLEM OF HERING CONCERNING ORTHOGONAL COVERS OF K-N

A Hering configuration of type k and order n is a factorization of the complete digraph K-n into n factors each of which consists of an isol ated vertex and the edge-disjoint union of directed k-cycles, which ha s the additional property that for any pair of distinct factors, say G (i) and G(j), there is precisely one pair of vertices, say {a, b}, suc h that G(i) contains the directed edge (a, b) and G(j) contains the di rected edge (b, a). Clearly a necessary condition for a Hering configu ration is n = 1 (mod k). It is shown here that for any fixed k, this c ondition is asymptotically, and, it is shown to be always sufficient f or k = 4. (C) 1995 Academic Press, Inc.