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arXiv · 2605.30048

Linear and matrix generalizations of some combinatorial min-max theorems

Nik Weaver
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Abstract

We review known linear and matrix generalizations of Hall's classic ``marriage theorem'' and K\H{o}nig's theorem on partial matchings in bipartite graphs, and relate them to linear and matrix generalizations of Dilworth's theorem about chains and antichains in posets and Menger's theorem about disjoint paths in directed graphs.

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Nik Weaver. 2026-05-28. Linear and matrix generalizations of some combinatorial min-max theorems. https://arxiv.org/abs/2605.30048

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