Average distance in bipartite tournaments

The average distance μ(D) of a strong digraph D is the average of the distances between all ordered pairs of distinct vertices of D. Plesník [3] proved that if D is a strong tournament of order n, then μ(D) ≤ n+4/6 + 1/n. In this paper we show that, asymptotically, the same inequality holds for strong bipartite tournaments. We also give an improved upper bound on the average distance of a k-connected bipartite tournament.