ALGEBRAIC COMBINATORICS

no. 4
Regularity of powers of edge ideals: from local properties to global bounds
Banerjee, Arindam1; Beyarslan, Selvi Kara2; Hà, Huy Tài3
1 Ramakrishna Mission Vivekananda Educational and Research Institute Belur, West Bengal, India
2 University of South Alabama Dept. of Mathematics and Statistics 411 University Boulevard North Mobile AL 36688-0002, USA
3 Tulane University Dept. of Mathematics 6823 St. Charles Ave. New Orleans LA 70118, USA
Algebraic Combinatorics, Volume 3 (2020) no. 4, pp. 839-854.

Let I=I(G) be the edge ideal of a graph G. We give various general upper bounds for the regularity function regI s , for s≥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 regI s =2s for all s≥2. This is a weaker version of a conjecture of Nevo and Peeva. Our method is to investigate the regularity function regI s , for s≥1, via local information of I.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.119
Classification: 05E40, 13A15, 13D02
Keywords: Castelnuovo–Mumford regularity, edge ideals, powers of ideals.
Banerjee, Arindam 1; Beyarslan, Selvi Kara 2; Hà, Huy Tài 3

1 Ramakrishna Mission Vivekananda Educational and Research Institute Belur, West Bengal, India
2 University of South Alabama Dept. of Mathematics and Statistics 411 University Boulevard North Mobile AL 36688-0002, USA
3 Tulane University Dept. of Mathematics 6823 St. Charles Ave. New Orleans LA 70118, USA
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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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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