On the Betti numbers of some classes of Binomial edge ideals
Zohaib Zahid, Sohail Zafar
TL;DR
This paper investigates the Betti numbers of binomial edge ideals for specific graph classes with high regularity, providing bounds on regularity based on induced subgraphs.
Contribution
It introduces new lower bounds for the Castelnuovo-Mumford regularity of arbitrary graphs using properties of binomial edge ideals.
Findings
Derived lower bounds for regularity based on induced subgraphs
Analyzed Betti numbers for certain graph classes with high regularity
Connected algebraic invariants to graph combinatorics
Abstract
We study the Betti numbers of binomial edge ideal associated to some classes of graphs with large Castelnuovo-Mumford regularity. As an application we give several lower bounds of the Castelnuovo-Mumford regularity of arbitrary graphs depending on induced subgraphs.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Polynomial and algebraic computation · Cholinesterase and Neurodegenerative Diseases