Necessary Condition for Path Partitioning Constraints
نویسندگان
چکیده
Given a directed graph G, the K node-disjoint paths problem consists in finding a partition of G into K node-disjoint paths, such that each path ends up in a given subset of nodes in 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 G, (2) the structure of each strongly connected component of 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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