A Graph Reduction Step Preserving Element-Connectivity and Applications

Chandra Chekuri, Nitish Korula

Abstract: Given an undirected graph G = (V,E) and subset of terminals T ⊆ V, the element-connectivity κ′ G (u,v) of two terminals u,v ∈ T is the maximum number of u-v paths that are pairwise disjoint in both edges and non-terminals V ∖ T (the paths need not be disjoint in terminals). Element-connectivity is more general than edge-connectivity and less general than vertex-connectivity. Hind and Oellermann [18] gave a graph reduction step that preserves the global element-connectivity of the graph. We show that this step also preserves local connectivity, that is, all the pairwise element-connectivities of the terminals.