Relation between regularity of powers of edge ideals and (im, reg)-invariant extension

2020/03/11 by Hiroju Kanno, Kanno, Hiroju
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2003.05419

openalex publication_date 2020/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we define (im, reg)-invariant extension of graphs and propose a new approach for Nevo and Peeva's conjecture which said that for any gap-free graph G with reg(I(G)) = 3 and for any k ≥ 2, I(G)^k has a linear resolution. Moreover, we consider new conjectures related to the regularity of powers of edge ideals of gap-free graphs.

Related

• Regularity of powers of edge ideals: from local properties to global\n bounds
• Characterization of graphs whose a small power of their edge ideals has a linear free resolution
• Gapfree graphs and powers of edge ideals with linear quotients
• Regularity of Edge Ideals and Their Powers
• Upper bounds for the regularity of powers of edge ideals of graphs