Let $D$ be some directed graph, and let $G$ and $G'$ be two acyclic subgraphs of $D$; let $E$ and $E'$ be their sets of edges. Is it possible to give a simple criterion on $E$ and $E'$ (sufficiency and necessity would be great, of course) for when the subgraph given by $E \cup E'$ is still acyclic?
(I can come up with [fairly trivial] necessary conditions, and also with [fairly elaborate] sufficient conditions, but all these are far from optimal.)
Thanks!
Edit: changed the wording and the title in response to Qiaochu Yuan's comments.