Neighborhood and degree conditions for super-edge-connected bipartite digraphs

A graph or digraph D is called super-λ, if every minimum edge cut consists of edges incident to or from a vertex of minimum degree, where λ is the edge-connectivity of D. Clearly, if D is super-λ, then λ = δ, where δ is the minimum degree of D. In this paper neighborhood, degree sequence, and degree conditions for bipartite graphs and digraphs to be super-λ are presented. In particular, the neighborhood condition generalizes the following result by Fiol 7]: If D is a bipartite digraph of order n and minimum degree δ ≥ max{3, ?(n + 3)/4?}, then D is super-λ.