The bounded twin-width conjecture for tournaments

Let $k\geq 1$. A tournament has twin-width at most $k$ if its twin-width is at most $k$. The bounded twin-width conjecture. The class of tournaments with twin-width at most $k$ is $\operatorname{\overrightarrow{\chi}}$-bounded. This asks whether bounded twin-width controls dichromatic number through the clique number; the paper gives examples showing that bounded twin-width does not imply bounded dichromatic number.