Bounds for the regularity of product of edge ideals

2019/08/28 by Banerjee, Arindam, Das, Priya, Selvaraja, S.
#05C70 #05E45 #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics #Primary: 13D02

paper · doi:10.48550/arxiv.1908.10573

Abstract

Let I and J be edge ideals in a polynomial ring R = \mathbbK[x₁,…,x_n] with I ⊆ J. In this paper, we obtain a general upper and lower bound for the Castelnuovo-Mumford regularity of IJ in terms of certain invariants associated with I and J. Using these results, we explicitly compute the regularity of IJ for several classes of edge ideals. Let J₁,…,J_d be edge ideals in a polynomial ring R with J₁ ⊆ ⋯ ⊆ J_d. Finally, we compute the precise expression for the regularity of J₁ J₂⋯ J_d when d ∈ \3,4\ and J_d is the edge ideal of complete graph.

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• Regularity and h-polynomials of edge ideals
• Regularity of Edge Ideals and Their Powers
• Upper bounds for the regularity of powers of edge ideals of graphs
• Bounded powers of edge ideals: regularity and linear quotients
• Joins, Ears and Castelnuovo-Mumford regularity