# ALGEBRAIC COMBINATORICS

Regularity of powers of edge ideals: from local properties to global bounds
Algebraic Combinatorics, Volume 3 (2020) no. 4, pp. 839-854.

Let $I=I\left(G\right)$ be the edge ideal of a graph $G$. We give various general upper bounds for the regularity function $\mathrm{reg}{I}^{s}$, for $s\ge 1$, addressing a conjecture made by the authors and Alilooee. When $G$ is a gap-free graph and locally of regularity 2, we show that $\mathrm{reg}{I}^{s}=2s$ for all $s\ge 2$. This is a weaker version of a conjecture of Nevo and Peeva. Our method is to investigate the regularity function $\mathrm{reg}{I}^{s}$, for $s\ge 1$, via local information of $I$.

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DOI: https://doi.org/10.5802/alco.119
Classification: 05E40,  13A15,  13D02
Keywords: Castelnuovo–Mumford regularity, edge ideals, powers of ideals.
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Banerjee, Arindam; Beyarslan, Selvi Kara; Hà, Huy Tài. Regularity of powers of edge ideals: from local properties to global bounds. Algebraic Combinatorics, Volume 3 (2020) no. 4, pp. 839-854. doi : 10.5802/alco.119. https://alco.centre-mersenne.org/articles/10.5802/alco.119/

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