DGGH's characterization conjecture for cop-win oriented graphs

An oriented graph $D$ is a directed graph obtained by orienting the edges of a simple undirected graph; a directed cycle is cop-dominated if the robber cannot avoid capture by entering it along some path and then repeatedly traveling around the cycle. DGGH's conjecture. An oriented graph $D$ is cop-win if and only if $D$ contains exactly one vertex of in-degree $0$, every vertex is reachable from that vertex, and every directed cycle of $D$ is cop-dominated.

The conjecture is attributed in the source to DGGH16. No resolution evidence is supplied in the paper excerpt.