Akbari–Dalirrooyfard–Ehsani–Ozeki–Sherkati conjecture on forbidden out-degrees

Let $G$ be a loopless $d$-regular graph, with parallel edges permitted, and let $F\subseteq\{0,1,\ldots,d\}$ be a list of forbidden out-degrees. An orientation is $F$-avoiding if no vertex has out-degree in $F$. Akbari–Dalirrooyfard–Ehsani–Ozeki–Sherkati conjecture. If $|F|<\tfrac{1}{2}d$, then $G$ admits an $F$-avoiding orientation. The bound is tight if true: $K_{2k+1}$ has no $F$-avoiding orientation for $F=\{k,\ldots,2k-1\}$. The conjecture is known for bipartite graphs, cliques, and regular graphs of degree at most $4$, while the general case remains open; the source proves it for $d=5,6$.