Geodesic
A linear algorithm for the two paths problem on permutation graphs
Discussiones Mathematicae. Graph Theory, Tome 15 (1995) no. 2, pp. 147-166.

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The 'two paths problem' is stated as follows. Given an undirected graph G = (V,E) and vertices s₁,t₁;s₂,t₂, the problem is to determine whether or not G admits two vertex-disjoint paths P₁ and P₂ connecting s₁ with t₁ and s₂ with t₂ respectively. In this paper we give a linear (O(|V|+ |E|)) algorithm to solve the above problem on a permutation graph.
Keywords: algorithm, bridge, connectivity, disjoint paths, permutation graph, two paths problem 
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Gopalakrishnan, C.; Pandu Rangan, C. A linear algorithm for the two paths problem on permutation graphs. Discussiones Mathematicae. Graph Theory, Tome 15 (1995) no. 2, pp. 147-166. http://geodesic.mathdoc.fr/item/DMGT_1995_15_2_a2/

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