Linear and matrix generalizations of some combinatorial min-max theorems
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910270249500672 |
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| author | Weaver, Nik |
| author_facet | Weaver, Nik |
| contents | We review known linear and matrix generalizations of Hall's classic ``marriage theorem'' and Kőnig'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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_30048 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Linear and matrix generalizations of some combinatorial min-max theorems Weaver, Nik Rings and Algebras Combinatorics Operator Algebras primary 15A03, 05C50, secondary 15A30, 05D15, 05C40 We review known linear and matrix generalizations of Hall's classic ``marriage theorem'' and Kőnig'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. |
| title | Linear and matrix generalizations of some combinatorial min-max theorems |
| topic | Rings and Algebras Combinatorics Operator Algebras primary 15A03, 05C50, secondary 15A30, 05D15, 05C40 |
| url | https://arxiv.org/abs/2605.30048 |