Regularity of Symbolic Powers of Edge Ideals

TL;DR

This paper investigates the regularity of symbolic powers of edge ideals in graphs, showing that for certain classes, their regularity matches that of ordinary powers, thus advancing understanding of algebraic properties of graph ideals.

Contribution

It establishes conditions under which the regularity of symbolic and ordinary powers of edge ideals are equal for specific graph classes.

Findings

Regularity of symbolic and ordinary powers coincide for certain graph classes.

Provides new insights into algebraic properties of edge ideals.

Enhances understanding of the relationship between symbolic and ordinary powers.

Abstract

In this article, we prove that for several classes of graphs, the Castelnuovo-Mumford regularity of symbolic powers of their edge ideals coincide with that of their ordinary powers.