Average distance in bipartite tournaments

The average distance p(D) of a strong digraph D is the average of the distances between all ordered pairs of distinct vertices of D. Plesnik [3] proved that if D is a strong tournament of order n, then mu(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.