Length 3 Edge-Disjoint Paths Is NP-Hard
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In 2003, it was claimed that the following problem was solvable in polynomial time: do there exist k edge-disjoint paths of length exactly 3 between vertices s and t in a given graph? The proof was flawed, and in this note we show that this problem is NP-hard. We use a reduction from Partial Orientation, a problem recently shown by Pálvölgyi to be NP-hard.
KeywordsEdge-disjoint paths NP-hardness NP-completeness network flow directed graph oriented graph degree sequence
Subject classification05C38 05C40 68Q25
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- Hannah Alpert & Jennifer Iglesias (2012). Length 3 Edge-Disjoint Paths and Partial Orientation. http://arxiv.org/abs/1201.6578v1.