  Let $D_k$ denote the tournament on $3k$ vertices consisting of three disjoint
vertex classes $V_1, V_2$ and $V_3$ of size $k$, each of which is oriented as a
transitive subtournament, and with edges directed from $V_1$ to $V_2$, from
$V_2$ to $V_3$ and from $V_3$ to $V_1$. Fox and Sudakov proved that given a
natural number $k$ and $\epsilon > 0$ there is $n_0(k,\epsilon )$ such that
every tournament of order $n_0(k,\epsilon )$ which is $\epsilon $-far from
being transitive contains $D_k$ as a subtournament. Their proof showed that
$n_0(k,\epsilon ) \leq \epsilon ^{-O(k/\epsilon ^2)}$ and they conjectured that
this could be reduced to $n_0(k,\epsilon ) \leq \epsilon ^{-O(k)}$. Here we
prove this conjecture.
