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arXiv · 2501.10918

A Min-Max Relation on Dicuts and Dijoins in Weighted Chordal Digraphs

Gérard Cornuéjols·Siyue Liu·R. Ravi
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Abstract

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.

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Gérard Cornuéjols, Siyue Liu, R. Ravi. 2026-05-30. A Min-Max Relation on Dicuts and Dijoins in Weighted Chordal Digraphs. https://arxiv.org/abs/2501.10918

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