  Scott asked the question of determining $c_d$ such that if $D$ is a digraph
with $m$ arcs and minimum outdegree $d\ge 2$ then $V(D)$ has a partition $V_1,
V_2$ such that $\min\left\{e(V_1,V_2),e(V_2, V_1)\right\}\geq c_dm$, where
$e(V_1,V_2)$ (respectively, $e(V_2,V_1)$) is the number of arcs from $V_1$ to
$V_2$ (respectively, from $V_2$ to $V_1$). Lee, Loh, and Sudakov showed that
$c_2=1/6+o(1)$ and $c_3=1/5+o(1)$, and conjectured that $c_d=
\frac{d-1}{2(2d-1)}+o(1)$ for $d\ge 4$. In this paper, we show $c_4=3/14+o(1)$
and prove some partial results for $d\ge 5$.
