computational complexity

, Volume 21, Issue 3, pp 511–513 | Cite as

Length 3 Edge-Disjoint Paths Is NP-Hard

  • Hannah AlpertEmail author
  • Jennifer Iglesias


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.


Edge-disjoint paths NP-hardness NP-completeness network flow directed graph oriented graph degree sequence 

Subject classification

05C38 05C40 68Q25 


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  1. Hannah Alpert & Jennifer Iglesias (2012). Length 3 Edge-Disjoint Paths and Partial Orientation.
  2. Andreas Bley (2003) On the complexity of vertex-disjoint length-restricted path problems. Comput. Complexity 12(3-4): 131–149 ISSN 1016-3328. doi: 10.1007/s00037-003-0179-6 MathSciNetzbMATHGoogle Scholar
  3. Dömötör Pálvölgyi (2009) Deciding soccer scores and partial orientations of graphs. Acta Univ. Sapientiae Math 1(1): 35–42. ISSN 1844-6094.MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer Basel AG 2012

Authors and Affiliations

  1. 1.Department of MathematicsMassachusetts Inst. of TechnologyCambridgeUSA
  2. 2.Department of MathematicsHarvey Mudd CollegeClaremontUSA

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