Edmonds–Giles weighted dijoin packing conjecture

Let $D=(V,A)$ be a digraph with arc weights $w i\{0,1\}^A$. The weight of a dicut is the \sum of the weights of its arcs, and the minimum dicut weight is the smallest such weight. The digraph packs $k$ dijoins if it has $k$ dijoins such that no arc $e$ belongs to more than $w(e)$ of them.

Edmonds–Giles conjecture. If the minimum weight of a dicut is $\tau$, then $D$ can pack $\tau$ dijoins.

The conjecture was disproved by Schrijver, so the corresponding weighted packing assertion is false; its unweighted version is Woodall's still-open conjecture.