A degree condition for cycles of maximum length in bipartite digraphs

We prove a sharp Ore-type criterion for hamiltonicity of balanced bipartite digraphs: for a≥2a≥2, a bipartite digraph DD with colour classes of cardinalities aa is hamiltonian if d+(u)+d−(v)≥a+2d+(u)+d−(v)≥a+2 whenever uu and vv lie in opposite colour classes and uv∉A(D)uv∉A(D).