Geometrically vertex decomposable open neighborhood ideals
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911391361794048 |
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| author | Lim, Jounglag |
| author_facet | Lim, Jounglag |
| contents | In this paper, we prove that the open neighborhood ideal of a TD-unmixed tree is geometrically vertex decomposable. This result implies that the associated Stanley-Reisner complex is vertex decomposable. We further demonstrate that Cohen-Macaulay open neighborhood ideals of trees are special cases of Cohen-Macaulay facet ideals of simplicial trees. Finally, we investigate open neighborhood ideals of chordal graphs and establish that almost all square-free monomial ideal can be realized as the open neighborhood ideal of a chordal graph. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_12886 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Geometrically vertex decomposable open neighborhood ideals Lim, Jounglag Commutative Algebra 13F55 (Primary), 05E40, 05C69 In this paper, we prove that the open neighborhood ideal of a TD-unmixed tree is geometrically vertex decomposable. This result implies that the associated Stanley-Reisner complex is vertex decomposable. We further demonstrate that Cohen-Macaulay open neighborhood ideals of trees are special cases of Cohen-Macaulay facet ideals of simplicial trees. Finally, we investigate open neighborhood ideals of chordal graphs and establish that almost all square-free monomial ideal can be realized as the open neighborhood ideal of a chordal graph. |
| title | Geometrically vertex decomposable open neighborhood ideals |
| topic | Commutative Algebra 13F55 (Primary), 05E40, 05C69 |
| url | https://arxiv.org/abs/2512.12886 |