A linear time algorithm for the arc disjoint Menger problem in planar directed graphs

Abstract

Given a graph G = (V, E) and two vertices s, t ∈ V, s ≠ t, the Menger problem is to find a maximum number of disjoint paths connecting s and t. Depending on whether the input graph is directed or not, and what kind of disjointness criterion is demanded, this general formulation is specialized to the directed or undirected vertex, and the edge or arc disjoint Menger problem, respectively.