Degree sequence conditions for maximally edge-connected and super-edge-connected digraphs depending on the clique number.

Let D be a finite and simple digraph with vertex set V ( D ) . For a vertex v ∈ V ( D ) , the degree d ( v ) of v is defined as the minimum value of its out-degree d + ( v ) and its in-degree d − ( v ) . If D is a graph or a digraph with minimum degree δ and edge-connectivity λ , then λ ≤ δ . A graph or a digraph is maximally edge-connected if λ = δ . A graph or a digraph is called super-edge-connected if every minimum edge-cut consists of edges adjacent to or from a vertex of minimum degree. In this note we present degree sequence conditions for maximally edge-connected and super-edge-connected digraphs depending on the clique number of the underlying graph. [ABSTRACT FROM AUTHOR]