A note on complete subdivisions in digraphs of large outdegree

Mader conjectured that for all there is an integer δ⁺() such that every digraph of minimum outdegree at least δ⁺() contains a subdivision of a transitive tournament of order . 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 d²/(8n3/2) .