Nash-Williams' well-balanced orientation conjecture

A graph is well-balanced oriented when it has an orientation in which, for every pair of vertices, the maximum number of edge-disjoint directed paths from the first vertex to the second equals the maximum number in the reverse direction. Nash-Williams' well-balanced orientation conjecture. Every graph admits a well-balanced orientation. This is one of the two general statements attributed to Nash-Williams that were historically left unproved; the supplied status evidence indicates that the associated orientation problem has since been resolved.