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arXiv · 1009.1472

Depth of edge rings arising from finite graphs

Takayuki Hibi·Akihiro Higashitani·Kyouko Kimura·Augustine B. O'Keefe
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Abstract

Let $G$ be a finite graph and $K[G]$ the edge ring of $G$. Based on the technique of Gröbner bases and initial ideals, it will be proved that, given integers $f$ and $d$ with $7 \leq f \leq d$, there exists a finite graph $G$ on $[d]={1,...,d}$ with $\depth K[G] = f$ and with $\Krull-dim K[G] = d$.

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Takayuki Hibi, Akihiro Higashitani, Kyouko Kimura, Augustine B. O'Keefe. 2010-09-08. Depth of edge rings arising from finite graphs. https://arxiv.org/abs/1009.1472

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