*PN* 95/9 TI On a problem of Hering concerning orthogonal covers of $\vec{K}_n$ AU Granville, A.; Gronau, H.-D.O.F.; Mullin, R.C. SO Preprint 95/9, ISSN 0948-1028 LA englisch AB A Hering configuration of type $k$ and order $n$ is a factorization of the complete digraph $\vec{K}_n$ into $n$ factors each of wich consists of an isolated vertex and the edge-disjoint union of directed $k$- cycles wich has the additional property that for any pair of distinct factors say $\vec{G}_i$ and $\vec{G}_j$ there is precisely one pair of vertices, say $\{a, b\}$ such that $\vec{G}_i$ contains the directed edge $(a, b)$ and $\vec{G}_j$ contains the directed edge $(b, a)$. Clearly a necessary condition for a Hering configuration is $n\equiv (\mbox{mod } k)$. It is shown here that for any fixed $k$, this condition is asymptotically sufficient, and, it is shown to be always sufficient for $k=4$ CC *05???* UT desings, covers of graph