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, ...

Researchers have proved a special case of the Erdős-Hajnal conjecture, which shows what happens in graphs that exclude anything resembling a pentagon. When you walk into a room full of people, you can ...