Erdős–Neumann-Lara conjecture for oriented graphs

Let $D$ be an oriented graph, and let $\Delta$ be the maximum degree of the underlying graph of $D$. Let $\vec{\chi}(D)$ denote its dichromatic number. Erdős–Neumann-Lara conjecture. Every oriented graph $D$ satisfies

$$\vec{\chi}(D)=O\left(\frac{\Delta}{\log \Delta}\right).$$

This is a directed analogue of Johansson's bound for triangle-free graphs and concerns the asymptotic relationship between dichromatic number and maximum degree. It remains open.