Regularity of powers of edge ideals: from local properties to global bounds

Arindam Banerjee, Selvi Kara, Huy Tai Ha

Let $I=I(G)$ be the edge ideal of a graph $G$. We give various general upper bounds for the regularity function $\text{reg}{I}^s$, for $s\ge 1$, addressing a conjecture made by t…