Regularity of Edge Ideals Via Suspension

Banerjee, Arindam; Nevo, Eran

doi:10.5802/alco.317

Banerjee, Arindam ¹; Nevo, Eran ²

¹ Indian Institute of Technology, Kharagpur
² Einstein Institute of Mathematics, The Hebrew University of Jerusalem.

Algebraic Combinatorics, Volume 6 (2023) no. 6, pp. 1687-1695.

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 $G$ , $reg (I {(G)}^{s}) \leq 2 s + reg I (G) - 2$ for all $s \geq 2$ , 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.

Received: 2022-12-29
Revised: 2023-05-20
Accepted: 2023-05-23
Published online: 2024-01-08

DOI: 10.5802/alco.317

Classification: 10X99, 14A12, 11L05
Keywords: Edge ideals, regularity, suspension

Author's affiliations:

Banerjee, Arindam ¹; Nevo, Eran ²

¹ Indian Institute of Technology, Kharagpur
² Einstein Institute of Mathematics, The Hebrew University of Jerusalem.

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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Banerjee, Arindam; Nevo, Eran. Regularity of Edge Ideals Via Suspension. Algebraic Combinatorics, Volume 6 (2023) no. 6, pp. 1687-1695. doi : 10.5802/alco.317. https://alco.centre-mersenne.org/articles/10.5802/alco.317/

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