Regularity of integral closures of edge ideals of weighted oriented graphs

TL;DR

This paper proves that the regularity of edge ideals of weighted oriented graphs does not increase when passing to their integral closures, providing insight into algebraic properties of these graph-associated ideals.

Contribution

It establishes a new monotonicity property of regularity under integral closure for edge ideals of weighted oriented graphs.

Findings

Regularity does not increase under integral closure.

Applicable to arbitrary weighted oriented graphs.

Enhances understanding of algebraic invariants of graph ideals.

Abstract

We prove that the regularity cannot increase when taking the integral closure for edge ideals of arbitrary weighted oriented graphs.