Upper bounds for the regularity of powers of edge ideals of graphs

2018/05/03 by A. V. Jayanthan, Jayanthan, A. V., S. Selvaraja +1 · 3 citations
Mathematics · #05C25 #13D02 #13F20 #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1805.01412

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

Abstract

Let G be a finite simple graph and I(G) denote the corresponding edge ideal. In this paper, we obtain upper bounds for the Castelnuovo-Mumford regularity of I(G)^q in terms of certain combinatorial invariants associated with G. We also prove a weaker version of a conjecture by Alilooee, Banerjee, Beyarslan and Hà on an upper bound for the regularity of I(G)^q and we prove the conjectured upper bound for the class of vertex decomposable graphs. Using these results, we explicitly compute the regularity of I(G)^q for several classes of graphs.

Cited by

• The Graded Betti Numbers of the Skeletons of Simplicial Complexes
• Local Cohomology and Degree Complexes of Monomial Ideals
• Symbolic powers of edge ideals of graphs

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