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For a connected graph G = (V, E), an edge set $${S\subset E}$$ is called a k-restricted edge cut if G − S is disconnected and every component of G − S contains at least k vertices. The k-restricted edge connectivity of G, denoted by λk(G), is defined as the cardinality of a minimum k-restricted edge cut. For two disjoint vertex sets $${U_1,U_2\subset V(G)}$$ , denote the set of edges of...
A digraph D is called super-arc-strongly connected if the arcs of every its minimum arc-disconnected set are incident to or from some vertex in D. A digraph without any directed cycle of length 2 is called an oriented graph. Sufficient conditions for digraphs to be super-arc-strongly connected have been given by several authors. However, closely related conditions for super-arc-strongly connected...
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