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Symbolic powers of edge ideals of graphs (1805.03428v2)
Published 9 May 2018 in math.AC
Abstract: Let $G$ be a graph and let $I = I(G)$ be its edge ideal. When $G$ is unicyclic, we give a decomposition of symbolic powers of $I$ in terms of its ordinary powers. This allows us to explicitly compute the Waldschmidt constant and the resurgence number of $I$. When $G$ is an odd cycle, we explicitly compute the regularity of $I{(s)}$ for all $s \in \mathbb{N}$. In doing so, we also give a natural lower bound for the regularity function $\text{reg } I{(s)}$, for $s \in \mathbb{N}$, for an arbitrary graph $G$.