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arXiv · 1907.02743

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

S. A. Seyed Fakhari
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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 $I(G)$.

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S. A. Seyed Fakhari. 2019-07-05. Regularity of symbolic powers of edge ideals of Cameron-Walker graphs. https://arxiv.org/abs/1907.02743

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