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

2018/05/03 by Arindam Banerjee, Banerjee, Arindam, Selvi Kara +3
Mathematics · #05C25 #05C70 #05E40 #13D02 #13F20 #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1805.01434

openalex publication_date 2018/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let I = I(G) be the edge ideal of a graph G. We give various general\nupper bounds for the regularity function \reg I^s, for s \≥ 1,\naddressing a conjecture made by the authors and Alilooee. When G is a\ngap-free graph and locally of regularity 2, we show that \reg I^s = 2s\nfor all s \≥ 2. This is a slightly weaker version of a conjecture of Nevo\nand Peeva. Our method is to investigate the regularity function\n\regI^s, for s \≥ 1, via local information of I.\n

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