Aharoni–Berger–Kfir conjecture on acyclic sets in oriented graphs

Let $D$ be an oriented graph with $n$ vertices and $m$ edges or arcs, and let $\vec{\alpha}(D)$ denote its largest acyclic set. Aharoni–Berger–Kfir conjecture.

$$\vec{\alpha}(D) \geq (1+o(1))\,\frac{n^2}{m} \log_2 \frac{m}{n}.$$

For tournaments this predicts $\vec{\alpha}(D)\geq (2+o(1))\log_2 n$; the bound is known up to a factor of $2$, and whether this factor can be attained is a major open problem.