  For $k \in \mathbb N$, Corr\'adi and Hajnal proved that every graph $G$ on
$3k$ vertices with minimum degree $\delta(G) \ge 2k$ has a $C_3$-factor, i.e.,
a partitioning of the vertex set so that each part induces the 3-cycle $C_3$.
Wang proved that every directed graph $\overrightarrow G$ on $3k$ vertices with
minimum total degree $\delta_t(\overrightarrow G):=\min_{v\in
V}(deg^-(v)+deg^+(v)) \ge 3(3k-1)/2$ has a $\overrightarrow C_3$-factor, where
$\overrightarrow C_3$ is the directed 3-cycle. The degree bound in Wang's
result is tight. However, our main result implies that for all integers $a \ge
1$ and $b \ge 0$ with $a+b=k$, every directed graph $\overrightarrow G$ on $3k$
vertices with minimum total degree $\delta_t(\overrightarrow G)\ge 4k-1$ has a
factor consisting of $a$ copies of $\overrightarrow T_3$ and $b$ copies of
$\overrightarrow C_3$, where $\overrightarrow T_3$ is the transitive tournament
on three vertices. In particular, using $b=0$, there is a $\overrightarrow
T_3$-factor of $\overrightarrow G $, and using $a=1$, it is possible to obtain
a $\overrightarrow C_3$-factor of $\overrightarrow G$ by reversing just one
edge of $\overrightarrow G$. All these results are phrased and proved more
generally in terms of undirected multigraphs.
  We conjecture that every directed graph $\overrightarrow G$ on $3k$ vertices
with minimum semidegree $\delta_0(\overrightarrow G):=\min_{v\in
V}\min(deg^-(v),deg^+(v)) \ge 2k$ has a $\overrightarrow C_3$-factor, and prove
that this is asymptotically correct.

Combinatorics