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arXiv · 1707.04874

Regularity of Powers of edge ideal of very well-covered graphs

Pooran Norouzi·Seyed Amin Seyed Fakhari·Siamak Yassemi
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Abstract

Let $k\geq 3$ be an integer and $G$ be a very well-covered graph with ${\rm odd-girth}(G)\geq 2k+1$. Assume that $I(G)$ is the edge ideal of $G$. We show that for every integer $s$ with $1\leq s\leq k-2$, we have ${\rm reg}(I(G)^s)=2s+\nu(G)-1$, where $\nu (G)$ is the induced matching number of $G$.

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Pooran Norouzi, Seyed Amin Seyed Fakhari, Siamak Yassemi. 2017-07-16. Regularity of Powers of edge ideal of very well-covered graphs. https://arxiv.org/abs/1707.04874

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