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arXiv · 2301.04763

Behaviors of pairs of dimensions and depths of edge ideals

Akihiro Higashitani·Akane Kanno·Ryota Ueji
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Abstract

Edge ideals of finite simple graphs $G$ on $n$ vertices are the ideals $I(G)$ of the polynomial ring $S$ in $n$ variables generated by the quadratic monomials associated with the edges of $G$. In this paper, we consider the possible pairs of dimensions and depths of $S/I(G)$ for connected graphs with a fixed number of vertices. We discuss such pairs in the case where dimension is relatively large. As a corollary, we completely determine the pairs for connected graphs with small number of vertices. We also study the possible pairs for connected chordal graphs.

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Akihiro Higashitani, Akane Kanno, Ryota Ueji. 2023-01-11. Behaviors of pairs of dimensions and depths of edge ideals. https://arxiv.org/abs/2301.04763

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