Graph spanners and connectivity

Abstract

Given an n-vertex graph or digraph G, a spanning subgraph S is a kspanner of G if for every u, v ε V(G), the distance from u to v in S is at most k times longer than the distance in G. This paper establishes some relationships between the connectivity and the existence of k-spanners with O(n) edges for graphs and digraphs. We give almost tight bounds of the connectivity of G which guarantees the existence of k-spanners with O(n) edges.