Akbari et al.'s conjecture on avoiding forbidden out-degree lists

Let $G$ be a graph, and let $F:V(G)\to 2^N$ assign a set of forbidden out-degrees to each vertex. An orientation $O$ of $G$ is $F$-avoiding if $d^+_O(v)\notin F(v)$ for every $v\in V(G)$. Akbari et al.'s conjecture. If

$$|F(v)|\leq \frac{1}{2}(d_G(v)-1)$$

for every $v\in V(G)$, then $G$ is $F$-avoiding. The conjecture strengthens the known bound $|F(v)|\leq d_G(v)/4$ for which an $F$-avoiding orientation is guaranteed; its resolution is not established in the supplied source.