**MSC:**- 05A99 None of the above but in this section

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 $k=4$