On the Meyniel condition for hamiltonicity in bipartite digraphs

We prove a sharp Meyniel-type criterion for hamiltonicity of a balanced bipartite digraph: For a ≥ 2, a strongly connected balanced bipartite digraph D on 2a vertices is hamiltonian if d(u) + d(v) ≥ 3a whenever uv / ∈ A(D) and vu / ∈ A(D). As a consequence, we obtain a sharp sufficient condition for hamiltonicity in terms of the minimal degree: a strongly connected balanced bipartite digraph D on 2a vertices is hamiltonian if δ(D) ≥ 3a/2.