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On Multiflow Lexicographics
2002
European journal of combinatorics (Print)
Given an undirected Eulerian network with the terminal-set {s} ∪ T , we call a vector ξ = (ξ(t) : t ∈ T ) feasible if there exists an integer maximum multiflow having exactly ξ(t) (s, t)-paths for each t ∈ T . This paper contributes to describing the set of feasible vectors. First, the feasible vectors are shown to be bases of a polymatroid (T, p) forming a proper part of the polytope defined by the supply-demand conditions; p(V ) = max{ξ(V ) : ξ ∈ }, V ⊆ T is described by a max-min theorem.
doi:10.1016/s0195-6698(02)90614-1
fatcat:uhdjtbdkrjcmtgntxszfpczfqa