Binomial edge ideals of regularity 3

2017/06/27 by Madani, Sara Saeedi, Kiani, Dariush · 1 citation
#Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics #Primary 13D02 #Secondary 05E40

paper · doi:10.48550/arxiv.1706.09002

Abstract

Let J_G be the binomial edge ideal of a graph G. We characterize all graphs whose binomial edge ideals, as well as their initial ideals, have regularity 3. Consequently we characterize all graphs G such that J_G is extremal Gorenstein. Indeed, these characterizations are consequences of an explicit formula we obtain for the regularity of the binomial edge ideal of the join product of two graphs. Finally, by using our regularity formula, we discuss some open problems in the literature. In particular we disprove a conjecture in \citeCDI on the regularity of weakly closed graphs.

Cited by

• Hilbert Coefficients and Regularity of Binomial Edge Ideals

Related

• On the regularity of binomial edge ideals
• The regularity of binomial edge ideals of graphs
• The Castelnuovo-Mumford regularity of binomial edge ideals
• A proof for a conjecture on the regularity of binomial edge ideals
• Regularity bounds for binomial edge ideals