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arXiv · 1805.04167

Edge ideals of oriented graphs

Huy Tài Hà·Kuei-Nuan Lin·Susan Morey·Enrique Reyes·Rafael H. Villarreal
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Abstract

Let $\mathcal{D}$ be a weighted oriented graph and let $I(\mathcal{D})$ be its edge ideal. Under a natural condition that the underlying (undirected) graph of $\mathcal{D}$ contains a perfect matching consisting of leaves, we provide several equivalent conditions for the Cohen-Macaulayness of $I(\mathcal{D})$. We also completely characterize the Cohen-Macaulayness of $I(\mathcal{D})$ when the underlying graph of $\mathcal{D}$ is a bipartite graph. When $I(\mathcal{D})$ fails to be Cohen-Macaulay, we give an instance where $I(\mathcal{D})$ is shown to be sequentially Cohen-Macaulay.

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Huy Tài Hà, Kuei-Nuan Lin, Susan Morey, Enrique Reyes, Rafael H. Villarreal. 2018-05-10. Edge ideals of oriented graphs. https://arxiv.org/abs/1805.04167

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