Given a digraph $D = (V, A)$ and $m \in \mathbb{N}$, the question is is there a subset $A' \subseteq A$, such that $\lvert A' \rvert \geq m$ and $d_{D'}^+(u) \leq d_{D'}^-(v)$ holds for every arc $(u, v) \in A'$ in the subgraph $D' = (V, A')$, i.e. the out-degree of $u$ is not larger than the in-degree of $v$? Note that the degree constraints should hold in the subgraph $D'$.This seems like a straight-forward problem, alas I am unable to connect it to some more familiar graph problem. I am mostly interested in its complexity.
Digraph problem relating in- and out-degrees
graphs;time complexity;decision problem