Minimal Free Resolutions of Edge Ideals of Edge-Weighted Complete Bipartite Graphs
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
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| _version_ | 1866911938442690560 |
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| author | Kubik, Bethany Tracy, Denise Rangel Sather-Wagstaff, Keri Ann |
| author_facet | Kubik, Bethany Tracy, Denise Rangel Sather-Wagstaff, Keri Ann |
| contents | We explicitly describe cellular minimal free resolutions of certain classes of edge ideals of weighted complete bipartite graphs based on a construction of Visscher. Specifically, we show that Visscher's construction minimally resolves all edge ideals of undirected vertex-weighted complete bipartite graphs, and we characterize the edge-weighted complete bipartite graphs whose edge ideals are minimally resolved by Visscher's construction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_00546 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Minimal Free Resolutions of Edge Ideals of Edge-Weighted Complete Bipartite Graphs Kubik, Bethany Tracy, Denise Rangel Sather-Wagstaff, Keri Ann Commutative Algebra We explicitly describe cellular minimal free resolutions of certain classes of edge ideals of weighted complete bipartite graphs based on a construction of Visscher. Specifically, we show that Visscher's construction minimally resolves all edge ideals of undirected vertex-weighted complete bipartite graphs, and we characterize the edge-weighted complete bipartite graphs whose edge ideals are minimally resolved by Visscher's construction. |
| title | Minimal Free Resolutions of Edge Ideals of Edge-Weighted Complete Bipartite Graphs |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2407.00546 |