On the directed Oberwolfach problem for complete symmetric equipartite digraphs and uniform-length cycles

We examine the necessary and sufficient conditions for a complete symmetric equipartite digraph Kn[m]* ${K}_{n[m]}<^>{* }$ with n $n$ parts of size m $m$ to admit a resolvable decomposition into directed cycles of length t $t$. We show that the obvious necessary conditions are sufficient for m,n,t & GE;2 $m,n,t\ge 2$ in each of the following four cases: (i) m(n-1) $m(n-1)$ is even; (ii) gcd(m,n)& NI;{1,3} $\text{gcd}(m,n)\notin \{1,3\}$; (iii) gcd(m,n)=1 $\text{gcd}(m,n)=1$ and 4 divide n $4| n$ or 6 divide n $6| n$; and (iv) gcd(m,n)=3 $\text{gcd}(m,n)=3$, and if n=6 $n=6$, then p divide m $p| m$ for a prime p & LE;37 $p\le 37$.