  Mader conjectured that for all k there is an integer d(k) such that every
digraph of minimum outdegree at least d(k) contains a subdivision of a
transitive tournament of order k. In this note we observe that if the minimum
outdegree of a digraph is sufficiently large compared to its order then one can
even guarantee a subdivision of a large complete digraph. More precisely, let G
be a digraph of order n whose minimum outdegree is at least d. Then G contains
a subdivision of a complete digraph of order at least d^2/(8n^{3/2}).

Combinatorics