  We consider the following problem posed by Volkmann in 2007: How close to
regular must a c-partite tournament be, to secure a strongly connected
subtournament of order $c$? We give sufficient conditions on the regularity of
balanced $c$-partite tournaments to assure the existence of strong maximal
subtournament with minimum degree at least $\left\lfloor
\frac{c-2}{4}\right\rfloor+1$. We obtain this result as an application of
counting the number of subtournaments of order $c$ for which a vertex has
minimum out-degree (resp. in-degree) at most $q\geq 0$.
