On multiflow lexicographics (Q1864616)

This paper is devoted to multiflow in Eulerian network. It contributes to describing the set \(R\) 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. \(p(V)= \max\{\xi(V):\xi\in R\}\), \(V\subseteq T\) is described by a max-min theorem. Second, the lexicographically minimum (and thereby maximum) feasible vector is found, for an arbitrary ordering of \(T\).