Given a directed graph \(\mathcal{G}\), the K node-disjoint paths problem consists in finding a partition of \(\mathcal{G}\) into K node-disjoint paths, such that each path ends up in a given subset of nodes in \(\mathcal{G}\). This article provides a necessary condition for the K node-disjoint paths problem which combines (1) the structure of the reduced graph associated with \(\mathcal{G}\), (2) the structure of each strongly connected component of \(\mathcal{G}\) with respect to dominance relation between nodes, and (3) the way the nodes of two strongly connected components are inter-connected. This necessary condition is next used to deal with a path partitioning constraint.


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Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Nicolas Beldiceanu
    • 1
  • Xavier Lorca
    • 1
  1. 1.École des Mines de Nantes, LINA FRE CNRS 2729, FR – 44307 Nantes Cedex 3 

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