Characterization of graphs whose a small power of their edge ideals has a linear free resolution

Nguyen Cong Minh, Thanh Vu

Let $I(G)$ be the edge ideal of a simple graph $G$. We prove that $I(G{)}^2$ has a linear free resolution if and only if $G$ is gap-free and reg$I(G)\le 3$. Similarly, we show that…