Determining all pairs edge connectivity of a 4-regular graph in O(|V|)

Summary form only given. The edge connectivity of a graph G = (V, E) is defined as the function, λ: V × V → N, that associates to any pair of vertices (u, v) the maximum number of edge-disjoint paths connecting the two vertices, λ(u, v). In this paper, we present a method for determining the function λ(u,v) for all vertex pairs in a 4-regular graph which achieves O(|V|) running time (with a small constant factor) and O(|V|) space complexity. We show with our method that determination and traversal of an Eulerian tour of each component of the 4-regular graph along with appropriate bookkeeping is enough for determining λ(u, v) for all pairs (u,v).