# Bounds on Regularity of Quadratic Monomial Ideals

## TL;DR

This paper explores combinatorial methods to establish bounds on the algebraic complexity of quadratic square-free monomial ideals, enhancing existing theoretical results with graph decomposition techniques.

## Contribution

It introduces new bounds on regularity using simple graph decompositions and structural graph theory, generalizing previous results.

## Key findings

- Improved bounds on regularity for quadratic square-free monomial ideals
- Application of graph decomposition techniques to algebraic problems
- Generalization of known bounds through combinatorial methods

## Abstract

Castelnuovo-Mumford regularity is a measure of algebraic complexity of an ideal. Regularity of monomial ideals can be investigated combinatorially. We use a simple graph decomposition and results from structural graph theory to prove, improve and generalize many of the known bounds on regularity of quadratic square-free monomial ideals.