2000 character limit reached
Regularity of symbolic powers of edge ideals of Cameron-Walker graphs (1907.02743v1)
Published 5 Jul 2019 in math.AC and math.CO
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 $s\geq 1$, 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 $I(G)$.