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

Pooran Norouzi, Seyed Amin Seyed Fakhari, Siamak Yassemi

Let $k\ge 3$ be an integer and $G$ be a very well-covered graph with $\mathrm{odd}-\mathrm{girth}(G)\ge 2k+1$. Assume that $I(G)$ is the edge ideal of $G$. We show that for every integer $s$…