Castelnuovo-Mumford regularity of generalized binomial edge ideals of graphs
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911352565530624 |
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| author | Kiani, Dariush Madani, Sara Saeedi Zhu, Guangjun |
| author_facet | Kiani, Dariush Madani, Sara Saeedi Zhu, Guangjun |
| contents | In this paper, we mainly study the Castelnuovo-Mumford regularity of the generalized binomial edge ideals of graphs. We show that this number can be any integer number from $2$ to $n-1$ where $n$ is the number of vertices in the underlying graph. We are able to show this, after giving some tight lower and upper bounds for the regularity of generalized binomial edge ideals of the join product of graphs. In particular, we characterize all generalized binomial edge ideals with the regularity equal to~$2$ as well as extremal Gorenstein ideals. For this purpose, we give a new combinatorial characterization for the class of $P_4$-free graphs. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_01120 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Castelnuovo-Mumford regularity of generalized binomial edge ideals of graphs Kiani, Dariush Madani, Sara Saeedi Zhu, Guangjun Commutative Algebra Combinatorics 05E40, 13D02 In this paper, we mainly study the Castelnuovo-Mumford regularity of the generalized binomial edge ideals of graphs. We show that this number can be any integer number from $2$ to $n-1$ where $n$ is the number of vertices in the underlying graph. We are able to show this, after giving some tight lower and upper bounds for the regularity of generalized binomial edge ideals of the join product of graphs. In particular, we characterize all generalized binomial edge ideals with the regularity equal to~$2$ as well as extremal Gorenstein ideals. For this purpose, we give a new combinatorial characterization for the class of $P_4$-free graphs. |
| title | Castelnuovo-Mumford regularity of generalized binomial edge ideals of graphs |
| topic | Commutative Algebra Combinatorics 05E40, 13D02 |
| url | https://arxiv.org/abs/2601.01120 |