Comparision between regularity of small symbolic powers and ordinary powers of an edge ideal

Nguyen Cong Minh, Le Dinh Nam, Thieu Dinh Phong +2

Let $G$ be a simple graph and $I$ its edge ideal. We prove that $$\mathrm{reg}(I^{(s)})=\mathrm{reg}(I^s)$$ for $s=2,3$, where $I^{(s)}$ is the $s$-th symbolic power of $I$. As a con…