A Polynomial Solution to the Undirected Two Paths Problem

Given an undirected graph G = (V, E) and vertices s,,tt; s2,t2, the problem is to determine whether or not G admits two vertex disjoint paths P, and P2 connecting s, with t, and s2 with t2, respectively. This problem is solved by an O(n.m) algorithm (n = IVJ, m = JElL An important by-product of the paper is a theorem stating that if G is 4-connected and nonplanar, then such paths P, and P2 exist for any choice of s,, s2, h, and t2 (as conjectured by Watkins). © 1980, ACM. All rights reserved.