Let be the edge ideal of a graph . We give various general upper bounds for the regularity function , for , addressing a conjecture made by the authors and Alilooee. When is a gap-free graph and locally of regularity 2, we show that for all . This is a weaker version of a conjecture of Nevo and Peeva. Our method is to investigate the regularity function , for , via local information of .
Revised: 2020-03-02
Accepted: 2020-03-18
Published online: 2020-08-20
Classification: 05E40, 13A15, 13D02
Keywords: Castelnuovo–Mumford regularity, edge ideals, powers of ideals.
@article{ALCO_2020__3_4_839_0, author = {Banerjee, Arindam and Beyarslan, Selvi Kara and H\`a, Huy T\`ai}, title = {Regularity of powers of edge ideals: from local properties to global bounds}, journal = {Algebraic Combinatorics}, pages = {839--854}, publisher = {MathOA foundation}, volume = {3}, number = {4}, year = {2020}, doi = {10.5802/alco.119}, language = {en}, url = {alco.centre-mersenne.org/item/ALCO_2020__3_4_839_0/} }
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/item/ALCO_2020__3_4_839_0/
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