On semi-transitive orientability of triangle-free graphs
Sergey Kitaev, A. V. Pyatkin · Discussiones Mathematicae Graph Theory · 2020
An orientation of a graph is semi-transitive if it is acyclic, and for any directed path $v_0\rightarrow v_1\rightarrow \cdots\rightarrow v_k$ either there is no arc between $v_0$ and $v_k$, or $v_i\rightarrow v_j$ is an arc for all $0\leq i