The domination-to-clique cluster conjecture

For a tournament $T$, let $\operatorname{dom}(T)$ be its domination number and let $\operatorname{\overrightarrow{\omega}}(T)$ be its clique number. The domination-to-clique cluster conjecture. There exist two functions $f$ and $\ell$ such that, for every integer $k$, every tournament $T$ with $\operatorname{dom}(T)\geq f(k)$ contains a subtournament $X$ with $|X|\leq\ell(k)$ and $\operatorname{\overrightarrow{\omega}}(X)\geq k$. The paper notes that this lies between the known domination-to-dichromatic cluster theorem and the stronger domination-to-domination cluster conjecture; it remains open.