On a Problem of Hering Concerning Orthogonal Covers of Kn

Abstract A Hering configuration of type k and order n is a factorization of the complete diagraph K n into n factors each of which consists of an isolated vertex and the edge-disjoint union of directed k -cycles, which has the additional property that for any pair of distinct factors, say G i , and G j , there is precisely one pair of vertices, say {ita, b}, such that G i contains the directed edge ( a, b ) and G j contains the directed edge ( b, a ). Clearly a necessary condition for a Hering configuration is n  1 (mod k ). It is shown here that for any fixed k , this condition is asymptotically, and, it is shown to be always sufficient for k = 4.