Pokrovskiy's strong tournament linking conjecture

A tournament is $r$-strong if deleting fewer than $r$ vertices leaves a strongly connected tournament, and its minimum in-degree and minimum out-degree are the least in-degree and out-degree among its vertices. A tournament is $k$-linked if, for every choice of distinct vertices $x_1,\ldots,x_k,y_1,\ldots,y_k$, there are pairwise vertex-disjoint directed paths from $x_i$ to $y_i$ for $i=1,\ldots,k$. Pokrovskiy's conjecture. For every natural number $k$ there exists an integer $d(k)$ such that every $2k$-strong tournament with minimum in-degree and minimum out-degree at least $d(k)$ is $k$-linked.

This conjecture proposes that sufficiently large minimum in-degree and out-degree, together with $2k$-strong connectivity, force $k$-linkedness in tournaments. The source presents it as a conjecture of Pokrovskiy; no resolution is given in the supplied text.