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arXiv · 2309.13568

The $\circ$ operation and $*$ operation of Cohen-Macaulay bipartite graphs

Yulong Yang·Guangjun Zhu·Yijun Cui·Shiya Duan
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Abstract

Let $G$ be a finite simple graph with the vertex set $V$ and let $I_G$ be its edge ideal in the polynomial ring $S=\mathbb{K}[x_V]$. In this paper, we compute the depth and the Castelnuovo--Mumford regularity of $S/I_G$ when $G=G_1\circ G_2$ or $G=G_1* G_2$ is a graph obtained from Cohen-Macaulay bipartite graphs $G_1$, $G_2$ by $\circ$ operation or $*$ operation, respectively.

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Yulong Yang, Guangjun Zhu, Yijun Cui, Shiya Duan. 2023-09-24. The $\circ$ operation and $*$ operation of Cohen-Macaulay bipartite graphs. https://arxiv.org/abs/2309.13568

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