Regularity of Edge Ideals Via Suspension

Arindam Banerjee; Eran Nevo

doi:10.5802/alco.317

Regularity of Edge Ideals Via Suspension

Arindam Banerjee, Eran Nevo

Einstein Institute of Mathematics

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Abstract

We study the Castelnuovo–Mumford regularity of powers of edge ideals for arbitrary (finite simple) graphs. It has been repeatedly conjectured that for every graph G, reg(I(G)^s) ≤ 2s + reg I(G) − 2 for all s ≥ 2, which is the best possible upper bound for any s. We prove this conjecture for every s for all bipartite graphs, and for s = 2 for all graphs. The s = 2 case is crucial for our work and suspension plays a key role in its proof.

Original language	English
Pages (from-to)	1687-1695
Number of pages	9
Journal	Algebraic Combinatorics
Volume	6
Issue number	6
DOIs	https://doi.org/10.5802/alco.317
State	Published - 2023

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© The author(s), 2023.

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Regularity of Edge Ideals Via Suspension

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