esech about KT-orientations

Problem statements

Let $G$ be a graph, and let $D$ be an orientation of $G$. We say that $D$ is a KT-orientation if for all $uv #34;in V(G)$, $D$ contains at most one directed path between $u$ and $v$ (in particular, $D$ contains no directed cycle).

Which graphs $G$ have a KT-orientation? (There are also some other problems about which graphs have orientations with nice properties that one might consider).