• Corpus ID: 15630914

Length 3 Edge-Disjoint Paths and Partial Orientation

@article{Alpert2012Length3E,
  title={Length 3 Edge-Disjoint Paths and Partial Orientation},
  author={Hannah Alpert and Jennifer Iglesias},
  journal={ArXiv},
  year={2012},
  volume={abs/1201.6578}
}
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 we show that this problem is NP-hard even if we disallow multiple edges. We use a reduction from Partial Orientation, a problem recently shown by Palvolgyi to be NP-hard. 

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Length 3 Edge-Disjoint Paths Is NP-Hard

This note shows that the problem of do there exist k edge-disjoint paths of length exactly 3 between vertices s and t in a given graph is NP-hard, using a reduction from Partial Orientation.

References

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Length 3 Edge-Disjoint Paths Is NP-Hard

This note shows that the problem of do there exist k edge-disjoint paths of length exactly 3 between vertices s and t in a given graph is NP-hard, using a reduction from Partial Orientation.

Deciding Soccer Scores and Partial Orientations of Graphs

We show that deciding if a simple graph has a partial ori- entation of its edges such that all vertices have a prescribed in-, out- and undirected degree, is NP-complete even for planar graphs. We

On the complexity of vertex-disjoint length-restricted path problems

  • A. Bley
  • Mathematics
    computational complexity
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It is proved that computing the maximum number of \vd \lb $s,t$-paths is \apx--complete for any length bound $\length\geq 5$ and that both problems are polynomially solvable.