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arXiv · 1605.00314

Graph Connectivity and Binomial Edge Ideals

Arindam Banerjee·Luis Núñez-Betancourt
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Abstract

We relate homological properties of a binomial edge ideal $\mathcal{J}_G$ to invariants that measure the connectivity of a simple graph $G$. Specifically, we show if $R/\mathcal{J}_G$ is a Cohen-Macaulay ring, then graph toughness of $G$ is exactly $\frac{1}{2}$. We also give an inequality between the depth of $R/\mathcal{J}_G$ and the vertex-connectivity of $G$. In addition, we study the Hilbert-Samuel multiplicity, and the Hilbert-Kunz multiplicity of $R/\mathcal{J}_G$.

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Arindam Banerjee, Luis Núñez-Betancourt. 2016-05-01. Graph Connectivity and Binomial Edge Ideals. https://arxiv.org/abs/1605.00314

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