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arXiv · 2410.00315

Lattice-Valued Bottleneck Duality

Robert Ghrist·Julian Gould·Miguel Lopez
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Abstract

This note reformulates certain classical combinatorial duality theorems in the context of order lattices. For source-target networks, we generalize bottleneck path-cut and flow-cut duality results to edges with capacities in a distributive lattice. For posets, we generalize a bottleneck version of Dilworth's theorem, again weighted in a distributive lattice. These results are applicable to a wide array of non-numerical network flow problems, as shown. All results, proofs, and applications were created in collaboration with AI language models. An appendix documents their role and impact.

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Robert Ghrist, Julian Gould, Miguel Lopez. 2024-10-01. Lattice-Valued Bottleneck Duality. https://arxiv.org/abs/2410.00315

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