Determining edge connectivity in 0(nm)

Abstract

We describe an algorithm that determines the edge connectivity of an n-vertex m-edge graph G in O(nm) time. A refinement shows that the question as to whether a graph is k-edge connected can be determined in O(kn2). For dense graphs characterized by m = Ω(n2), the latter result implies that determination of whether a graph is k-edge connected for any fixed k can be accomplished in time linear in input size.