A linear-time algorithm for finding a sparse k-connected spanning subgraph of a k-connected graph

Abstract

We show that any k-connected graph G = (V, E) has a sparse k-connected spanning subgraph G′ = (V, E′) with |E′| =O(k|V|) by presenting an O(|E|)-time algorithm to find one such subgraph, where connectivity stands for either edge-connectivity or node-connectivity. By using this algorithm as preprocessing, the time complexities of some graph problems related to connectivity can be improved. For example, the current best time bound O(max{k2|V|1/2, k|V|}|E|) to determine whether node-connectivity K(G) of a graph G = (V, E) is larger than a given integer k or not can be reduced to O(max{k3|V|3/2, k2|V|2}). © 1992 Springer-Verlag New York Inc.