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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1013,
author = {C.P. Gopalakrishnan and C. Pandu Rangan},
title = {A linear algorithm for the two paths problem on permutation graphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {15},
year = {1995},
pages = {147-166},
zbl = {0845.05085},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1013}
}
C.P. Gopalakrishnan; C. Pandu Rangan. A linear algorithm for the two paths problem on permutation graphs. Discussiones Mathematicae Graph Theory, Tome 15 (1995) pp. 147-166. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1013/
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