  A tantalizing open problem, posed independently by Stiebitz in 1995 and by
Alon in 2006, asks whether for every pair of integers $s,t \ge 1$ there exists
a finite number $F(s,t)$ such that the vertex set of every digraph of minimum
out-degree at least $F(s,t)$ can be partitioned into non-empty parts $A$ and
$B$ such that the subdigraphs induced on $A$ and $B$ have minimum out-degree at
least $s$ and $t$, respectively.
  In this short note, we prove that if $F(2,2)$ exists, then all the numbers
$F(s,t)$ with $s,t\ge 1$ exist and satisfy $F(s,t)=\Theta(s+t)$. In
consequence, the problem of Alon and Stiebitz reduces to the case $s=t=2$.
Moreover, the numbers $F(s,t)$ with $s,t \ge 2$ either all exist and grow
linearly, or all of them do not exist.
