In a digraph, a dicut is a cut where all the arcs cross in one direction. A dijoin is a subset of arcs that intersects every dicut. Edmonds and Giles conjectured that in a weighted digraph, the minimum weight of a dicut is equal to the maximum size of a packing of dijoins. This has been disproved. However, the unweighted version conjectured by Woodall remains open. We prove that the Edmonds-Giles conjecture is true if the underlying undirected graph is chordal. We also give a strongly polynomial-time algorithm to construct such a packing.

翻译：在有向图中，对偶截是指所有弧均沿同一方向穿越的截。对偶连接是与每个对偶截相交的弧子集。Edmonds和Giles猜想：在加权有向图中，对偶截的最小权重等于对偶连接打包的最大规模。该猜想已被证伪。然而，Woodall提出的无权重版本仍为开放问题。我们证明：若底层无向图为弦图，则Edmonds-Giles猜想成立。此外，我们给出一个强多项式时间算法用于构造此类打包。