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 ≥ 2 , a bipartite digraph D with colour classes of cardinalities a is hamiltonian if d + ( u ) + d − ( v ) ≥ a + 2 whenever u and v lie in opposite colour classes and u v ∉ A ( D ) .