Packing Dijoins in Weighted Chordal Digraphs
Combinatorics
2025-01-22 v1 Data Structures and Algorithms
Optimization and Control
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.
Keywords
Cite
@article{arxiv.2501.10918,
title = {Packing Dijoins in Weighted Chordal Digraphs},
author = {Gérard Cornuéjols and Siyue Liu and R. Ravi},
journal= {arXiv preprint arXiv:2501.10918},
year = {2025}
}