Alon–Yuster conjecture on orientations avoiding directed triangles

Given a graph $G$ and an oriented graph $\vec H$, let $D(G,\vec H)$ be the number of orientations of $G$ containing no copy of $\vec H$, and define

$$D(n,\vec H)=\max\{D(G,\vec H):G\text{ is an }n\text{-vertex graph}\}.$$

Let $K^\circlearrowright_3$ denote the strongly connected orientation of a triangle. Alon–Yuster's conjecture. For $n\geq 1$,

$$D(n,K^\circlearrowright_3)=\max\{2^{\lfloor n^2/4\rfloor},n!\}.$$

The conjecture was posed by Alon and Yuster after they established the corresponding extremal behavior for sufficiently large $n$ and computed the values for small $n$. The paper confirms the conjecture and further shows that the balanced complete bipartite graph is the unique $n$-vertex extremal graph when the value is $2^{\lfloor n^2/4\rfloor}$, so the claim is solved.