Abstract
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.
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Hellwig, A., Volkmann, L. Neighborhood and degree conditions for super-edge-connected bipartite digraphs. Results. Math. 45, 45–58 (2004). https://doi.org/10.1007/BF03322996
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DOI: https://doi.org/10.1007/BF03322996