Regularity of Edge Ideals Via Suspension

Arindam Banerjee, Eran Nevo

Research output: Contribution to journalArticlepeer-review

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 languageAmerican English
Pages (from-to)1687-1695
Number of pages9
JournalAlgebraic Combinatorics
Volume6
Issue number6
DOIs
StatePublished - 2023

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Publisher Copyright:
© The author(s), 2023.

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