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About this paper
Gérard Cornuéjols, Siyue Liu, R. Ravi
Researchers at Carnegie Mellon University proved the Edmonds-Giles conjecture holds for weighted digraphs where the underlying undirected graph is chordal, providing a constructive proof and a strongly polynomial-time algorithm for finding the maximum packing of dijoins.
Key insights
- All known counterexamples to the Edmonds-Giles conjecture feature large chordless cycles (length at least 6) in their underlying undirected graphs, motivating the focus on chordal graphs (which lack chordless cycles longer than 3).
- Chordal graphs' structural properties, specifically the existence of simplicial vertices, enable a robust inductive proof strategy for the conjecture.
- A precise weight redistribution mechanism is essential to ensure that the minimum dicut value in the reduced graph remains consistent with the original graph, allowing for successful induction.
Summary by alphaXiv.
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