Alon's partition conjecture for digraphs

Let $D$ be a digraph, let $D\langle V_i\rangle$ denote the subdigraph induced by $V_i$, and let $k$ be a positive integer. Alon's partition conjecture. There exists a function $h$ such that every digraph with minimum out-degree at least $h(k)$ has a partition $(V_1,V_2)$ for which each $D\langle V_i\rangle$, $i=1,2$, has minimum out-degree at least $k$. The source says that even the existence of $h(2)$ remains open; if true, the conjecture would imply closure of the class of $\delta^+$-maderian digraphs under disjoint union.