Regularity of powers of edge ideals: from local properties to global bounds
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 s1, 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 s2. This is a weaker version of a conjecture of Nevo and Peeva. Our method is to investigate the regularity function regI s , for s1, via local information of I.

Received: 2019-04-07
Revised: 2020-03-02
Accepted: 2020-03-18
Published online: 2020-08-20
DOI: https://doi.org/10.5802/alco.119
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},
     publisher = {MathOA foundation},
     volume = {3},
     number = {4},
     year = {2020},
     pages = {839-854},
     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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