The planar maximum-degree-four characterization of semi-transitive line graphs

Let $G$ be a graph, let $L(G)$ denote its line graph, and let $\Delta(G)$ denote its maximum degree. An orientation is semi-transitive when it is acyclic and has no shortcuts. Planar line-graph characterization. The line graph $L(G)$ is semi-transitively orientable if and only if $G$ is planar and $\Delta(G)\leq 4$.

This is presented in the paper's conclusion as a conjecture arising from the preceding results. The source does not provide a resolution, so the characterization remains open here.