Gorenstein and Cohen-Macaulay Matching Complexes
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arXiv
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866913308722855936 |
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| author | Nikseresht, Ashkan |
| author_facet | Nikseresht, Ashkan |
| contents | Let $H$ be a simple undirected graph. The family of all matchings of $H$ forms a simplicial complex called the matching complex of $H$. Here , we give a classification of all graphs with a Gorenstein matching complex. Also we study when the matching complex of $H$ is Cohen-Macaulay and, in certain classes of graphs, we fully characterize those graphs which have a Cohen-Macaulay matching complex. In particular, we characterize when the matching complex of a graph with girth at least 5 or a complete graph is Cohen-Macaulay. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2106_13993 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Gorenstein and Cohen-Macaulay Matching Complexes Nikseresht, Ashkan Commutative Algebra Combinatorics 13F55, 05E40, 05E45 Let $H$ be a simple undirected graph. The family of all matchings of $H$ forms a simplicial complex called the matching complex of $H$. Here , we give a classification of all graphs with a Gorenstein matching complex. Also we study when the matching complex of $H$ is Cohen-Macaulay and, in certain classes of graphs, we fully characterize those graphs which have a Cohen-Macaulay matching complex. In particular, we characterize when the matching complex of a graph with girth at least 5 or a complete graph is Cohen-Macaulay. |
| title | Gorenstein and Cohen-Macaulay Matching Complexes |
| topic | Commutative Algebra Combinatorics 13F55, 05E40, 05E45 |
| url | https://arxiv.org/abs/2106.13993 |