Regularity of symbolic powers of edge ideals of chordal graphs

Abstract

Assume that G is a chordal graph with edge ideal $I(G)$ and induced matching number $\mathrm{\nu }(G)$. We denote the sth symbolic power of $I(G)$ by $I{(G)}^{(s)}$. It is shown that $\mathrm{reg}(I{(G)}^{(s)})=2s+\mathrm{\nu }(G)-1$ for every integer $s\ge 1$.