How to make a strongly connected digraph two-connected
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 [FJ1] and [Jor3] by some structural statements related to families of ordered pairs of subsets.
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