On multiflow lexicographics

Michael Lomonosov

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


Given an undirected Eulerian network with the terminal-set {s} U 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 Ξ 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 ∈ Ξ}, V ⊆ T is described by a max-min theorem. The question whether Ξ contains all the integer bases, thereby admitting a polyhedral description, remains open. Second, the lexicographically minimum (and thereby maximum) feasible vector is found, for an arbitrary ordering of T. The results are based on the integrality theorem of A. Karzanov and Y. Manoussakis (Minimum (2, r)-metrics and integer multiflows, Europ. J. Combinatorics (1996) 17, 223-232) but we develop an original approach, also providing an alternative proof to this theorem.

Original languageEnglish
Pages (from-to)1043-1054
Number of pages12
JournalEuropean Journal of Combinatorics
Issue number8
StatePublished - 1 Jan 2002

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics


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