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, ...

We study the asymptotics of large, moderate and normal deviations for the connected components of the sparse random graph by the method of stochastic processes. We obtain the logarithmic asymptotics ...