Compatible Forts and Maximum Nullity of a Graph
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913416356036608 |
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| author | Furst, Veronika Hutchens, John Mitchell, Lon Zhang, Yaqi |
| author_facet | Furst, Veronika Hutchens, John Mitchell, Lon Zhang, Yaqi |
| contents | We consider bounds on maximum nullity of a graph via transversal numbers of compatible collections of forts. Results include generalizations of theorems from symmetric to combinatorially symmetric matrices, special bases of matrix nullspaces derived from transversal sets, and examples of issues that arise when considering only minimal forts and how to avoid them. We also show an important difference between constructing symmetric and combinatorially symmetric matrices associated to a graph whose nullspaces are supported on collections of disjoint forts. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_03492 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Compatible Forts and Maximum Nullity of a Graph Furst, Veronika Hutchens, John Mitchell, Lon Zhang, Yaqi Combinatorics 05C50 (Primary), 15A18, 15A03, 05B35 (Secondary) We consider bounds on maximum nullity of a graph via transversal numbers of compatible collections of forts. Results include generalizations of theorems from symmetric to combinatorially symmetric matrices, special bases of matrix nullspaces derived from transversal sets, and examples of issues that arise when considering only minimal forts and how to avoid them. We also show an important difference between constructing symmetric and combinatorially symmetric matrices associated to a graph whose nullspaces are supported on collections of disjoint forts. |
| title | Compatible Forts and Maximum Nullity of a Graph |
| topic | Combinatorics 05C50 (Primary), 15A18, 15A03, 05B35 (Secondary) |
| url | https://arxiv.org/abs/2407.03492 |