ALGEBRAIC COMBINATORICS

no. 6
Regularity of Edge Ideals Via Suspension
Banerjee, Arindam1; Nevo, Eran2
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.

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+regI(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.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.317
Classification: 10X99, 14A12, 11L05
Keywords: Edge ideals, regularity, suspension
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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