Regularity of powers of edge ideals: from local properties to global bounds

Banerjee, Arindam; Beyarslan, Selvi Kara; Hà, Huy Tài

doi:10.5802/alco.119

Banerjee, Arindam ; Beyarslan, Selvi Kara ; Hà, Huy Tài

Algebraic Combinatorics, Volume 3 (2020) no. 4, pp. 839-854.

Abstract

Let $I = I (G)$ be the edge ideal of a graph $G$ . We give various general upper bounds for the regularity function $reg I^{s}$ , for $s \geq 1$ , addressing a conjecture made by the authors and Alilooee. When $G$ is a gap-free graph and locally of regularity 2, we show that $reg I^{s} = 2 s$ for all $s \geq 2$ . This is a weaker version of a conjecture of Nevo and Peeva. Our method is to investigate the regularity function $reg I^{s}$ , for $s \geq 1$ , 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.

BibTeX
RIS

@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 = {https://alco.centre-mersenne.org/articles/10.5802/alco.119/}
}

TY  - JOUR
AU  - Banerjee, Arindam
AU  - Beyarslan, Selvi Kara
AU  - Hà, Huy Tài
TI  - Regularity of powers of edge ideals: from local properties to global bounds
JO  - Algebraic Combinatorics
PY  - 2020
DA  - 2020///
SP  - 839
EP  - 854
VL  - 3
IS  - 4
PB  - MathOA foundation
UR  - https://alco.centre-mersenne.org/articles/10.5802/alco.119/
UR  - https://doi.org/10.5802/alco.119
DO  - 10.5802/alco.119
LA  - en
ID  - ALCO_2020__3_4_839_0
ER  -

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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