Using expander graphs to find vertex connectivity

The (vertex) connectivity κ of a graph is the smallest number of vertices whose deletion separates the graph or makes it trivial. We present the fastest known algorithm for finding κ. For a digraph with n vertices, m edges and connectivity κ the time bound is O((n+min(κ^5/2,κn^3/4))m). This improves the previous best bound of O((n+min(κ³,κn))m). For an undirected graph both of these bounds hold with m replaced κn. Our approach uses expander graphs to exploit nesting properties of certain separation triples