Cohen-Macaulayness of powers of edge ideals of edge-weighted graphs
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917916218228736 |
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| author | Li, Jiaxin Trung, Tran Nam Zhu, Guangjun |
| author_facet | Li, Jiaxin Trung, Tran Nam Zhu, Guangjun |
| contents | In this paper, we characterize the Cohen-Macaulayness of the second power $I(G_ω)^2$ of the weighted edge ideal $I(G_ω)$ when the underlying graph $G$ is a very well-covered graph. We also characterize the Cohen-Macaulayness of all ordinary powers of $I(G_ω)^n$ when $G$ is a tree with a perfect matching consisting of pendant edges and the induced subgraph $G[V(G)\setminus S]$ of $G$ on $V(G)\setminus S$ is a star, where $S$ is the set of all leaf vertices, or if $G$ is a connected graph with a perfect matching consisting of pendant edges and the induced subgraph $G[V(G)\setminus S]$ of $G$ on $V(G)\setminus S$ is a complete graph and the weight function $ω$ satisfies $ω(e)=1$ for all $e\in E(G[V(G)\setminus S])$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_04872 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cohen-Macaulayness of powers of edge ideals of edge-weighted graphs Li, Jiaxin Trung, Tran Nam Zhu, Guangjun Commutative Algebra Primary 13C15, 13C14, Secondary 05E40, 13F20 In this paper, we characterize the Cohen-Macaulayness of the second power $I(G_ω)^2$ of the weighted edge ideal $I(G_ω)$ when the underlying graph $G$ is a very well-covered graph. We also characterize the Cohen-Macaulayness of all ordinary powers of $I(G_ω)^n$ when $G$ is a tree with a perfect matching consisting of pendant edges and the induced subgraph $G[V(G)\setminus S]$ of $G$ on $V(G)\setminus S$ is a star, where $S$ is the set of all leaf vertices, or if $G$ is a connected graph with a perfect matching consisting of pendant edges and the induced subgraph $G[V(G)\setminus S]$ of $G$ on $V(G)\setminus S$ is a complete graph and the weight function $ω$ satisfies $ω(e)=1$ for all $e\in E(G[V(G)\setminus S])$. |
| title | Cohen-Macaulayness of powers of edge ideals of edge-weighted graphs |
| topic | Commutative Algebra Primary 13C15, 13C14, Secondary 05E40, 13F20 |
| url | https://arxiv.org/abs/2502.04872 |