Let G = (V(G), E(G)) be a graph. A set S ⊆ E(G) is an edge k-cut in G if the graph G − S = (V(G), E(G) \ S) has at least k connected components. The generalized k-edge connectivity of a graph G, ...

In 1950 Edward Nelson, then a student at the University of Chicago, asked the kind of deceptively simple question that can give mathematicians fits for decades. Imagine, he said, a graph — a ...