In this paper we consider the following problem. Given an undirected graph G = (V,E) and vertices s₁,t₁;s₂,t₂, the problem is to determine whether or not G admits two edge-disjoint paths P₁ and P₂ connecting s₁ with t₁ and s₂ with t₂, respectively. We give a linear (O(|V|+|E|)) algorithm to solve this problem on a permutation graph.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1007,
author = {C. P. Gopalakrishnan and C. Pandu Rangan},
title = {Edge-disjoint paths in permutation graphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {15},
year = {1995},
pages = {59-72},
zbl = {0828.05057},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1007}
}
C. P. Gopalakrishnan; C. Pandu Rangan. Edge-disjoint paths in permutation graphs. Discussiones Mathematicae Graph Theory, Tome 15 (1995) pp. 59-72. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1007/
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