Regularity of symbolic powers of edge ideals of Cameron-Walker graphs

Abstract

A Cameron-Walker graph is a graph for which the matching number and the induced matching number are the same. Assume that $G$ is a Cameron-Walker graph with edge ideal $I(G)$, and let $\ind-match(G)$ be the induced matching number of $G$. It is shown that for every integer $s\ge 1$, we have the equality ${\rm reg}(I(G)^{(s)})=2s+\ind-match(G)-1$, where $I(G{)}^{(s)}$ denotes the $s$-th symbolic power of $I(G)$.

Cited by in corpus (1)

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