How to make a strongly connected digraph two-connected

Abstract

Given a strongly connected digraph, we give a combinatorial polynomial algorithm for determining a smallest set of new edges to be added to make the graph 2-vertex-connected. The problem was shown to be polynomially solvable in a recent paper [FJ1] for arbitrary starting digraph and any target connectivity k ≥ 1. However, the algorithm relied on the ellipsoid method. Here we further simplify the results of IF J1] and [Jor3] by some structural statements related to families of ordered pairs of subsets.