Spring 2023 IMPROVED BOUNDS FOR THE REGULARITY OF POWERS OF EDGE IDEALS OF GRAPHS
Seyed Amin Seyed Fakhari, Siamak Yassemi
J. Commut. Algebra 15(1): 85-98 (Spring 2023). DOI: 10.1216/jca.2023.15.85

Abstract

Let G be a graph with edge ideal I(G). We recall the notions, given by Seyed Fakhari and Yassemi (2018), of min-match{K2,C5}(G) and ind-match{K2,C5}(G). We show that

reg(I(G)s)2s+min-match{K2,C5}(G)1,

for all s1, which implies that

reg(I(G)s)2s+min-match(G)1.

Moreover, we show that

reg(I(G)s)2s+ind-match{K2,C5}(G)2,

and if ind-match{K2,C5}(G) is an odd integer, then

reg(I(G)s)2s+ind-match{K2,C5}(G)1.

As a consequence, we estimate the regularity of powers of edge ideals of Cohen–Macaulay graphs with girth(G)5. Furthermore, it is shown that

reg(I(G)s)2s+ord-match(G)1,

where ord-match(G) denotes the ordered matching number of G.

Citation

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Seyed Amin Seyed Fakhari. Siamak Yassemi. "IMPROVED BOUNDS FOR THE REGULARITY OF POWERS OF EDGE IDEALS OF GRAPHS." J. Commut. Algebra 15 (1) 85 - 98, Spring 2023. https://doi.org/10.1216/jca.2023.15.85

Information

Received: 9 August 2021; Revised: 27 November 2021; Accepted: 8 December 2021; Published: Spring 2023
First available in Project Euclid: 20 June 2023

MathSciNet: MR4604788
zbMATH: 1519.05115
Digital Object Identifier: 10.1216/jca.2023.15.85

Subjects:
Primary: 05E99 , 13D02

Keywords: Castelnuovo–Mumford regularity , cochordal cover number , Edge ideal , induced matching number , ordered matching number

Rights: Copyright © 2023 Rocky Mountain Mathematics Consortium

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Vol.15 • No. 1 • Spring 2023
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