A Short Note on Relevant Cuts
Combinatorics
2026-03-04 v3
Abstract
The set of relevant cuts in a graph is the union of all minimum weight bases of the cut space. A cut is relevant if and only if it is the a minimum weight cut between two distinct vertices. Moreover, we give a characterization in terms of Picard-Queyranne Directed Acyclic Graphs that can be used to accelerate the enumeration of the relevant cuts. Finally, we perform an experimental evaluation by comparing with state-of-the-art algorithms.
Keywords
Cite
@article{arxiv.2410.20257,
title = {A Short Note on Relevant Cuts},
author = {Nico Domschke and Thomas Gatter and Richard Golnik and Peter F. Stadler},
journal= {arXiv preprint arXiv:2410.20257},
year = {2026}
}
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10 pages