An Upper Bound for the Regularity of Symbolic Powers of Edge Ideals of Chordal Graphs

Abstract

Assume that $G$ is a chordal graph with edge ideal $I(G)$ and ordered matching number $\nu_{o}(G)$. For every integer $s\geq 1$, we denote the $s$-th symbolic power of $I(G)$ by $I(G)^{(s)}$. It is shown that ${\rm reg}(I(G)^{(s)})\leq 2s+\nu_{o}(G)-1$. As a consequence, we determine the regularity of symbolic powers of edge ideals of chordal Cameron-Walker graphs.