Linear and matrix generalizations of some combinatorial min-max theorems
math.RAmath.COmath.OA2026-05v1license
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.
Comments: 25 pages
Cite
@article{arxiv.2605.30048,
title = {Linear and matrix generalizations of some combinatorial min-max theorems},
author = {Nik Weaver},
journal= {arXiv preprint arXiv:2605.30048},
year = {2026}
}