Woodall’s unweighted dijoin-packing conjecture

Prove that, in every unweighted digraph, the minimum size of a dicut equals the maximum number of pairwise disjoint dijoins.

Background

The paper defines a dijoin as a set of arcs intersecting every dicut and explains that the weighted Edmonds–Giles equality fails in general because of known counterexamples. Woodall’s unweighted version removes arc capacities and asks whether the minimum cardinality of a dicut equals the maximum number of disjoint dijoins. The paper’s chordal-graph theorem establishes this equality for a substantial graph class but does not resolve the conjecture for arbitrary digraphs.