Resolution and Betti numbers of Vertex cover ideals
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911827330334720 |
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| author | Hà, Tài Huy Hibi, Takayuki |
| author_facet | Hà, Tài Huy Hibi, Takayuki |
| contents | The vertex cover ideal $J(G)$ of a finite graph $G$ is studied. We characterize when a Cohen--Macaulay vertex cover ideal $J(G)$ has a Scarf minimal free resolution. Furthermore, by using both combinatorial and topological techniques, the graded Betti number $β_{i,i+j}(J(G))$, where $i$ and $j$ are the projective dimension and the regularity of $J(G)$, is computed, when $G$ is either a path or a cycle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_01001 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Resolution and Betti numbers of Vertex cover ideals Hà, Tài Huy Hibi, Takayuki Commutative Algebra The vertex cover ideal $J(G)$ of a finite graph $G$ is studied. We characterize when a Cohen--Macaulay vertex cover ideal $J(G)$ has a Scarf minimal free resolution. Furthermore, by using both combinatorial and topological techniques, the graded Betti number $β_{i,i+j}(J(G))$, where $i$ and $j$ are the projective dimension and the regularity of $J(G)$, is computed, when $G$ is either a path or a cycle. |
| title | Resolution and Betti numbers of Vertex cover ideals |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2404.01001 |