Algebraic discrete Morse theory for the hull resolution

TL;DR

This paper explores the application of algebraic discrete Morse theory to hull resolutions, identifying specific cases where it can produce minimal resolutions for edge ideals of certain graphs.

Contribution

It characterizes all instances where algebraic discrete Morse theory yields minimal hull resolutions for edge ideals of the complement of triangle-free graphs.

Findings

Identifies cases where hull resolutions are minimal using algebraic discrete Morse theory.

Provides a complete characterization for triangle-free graph complements.

Enhances understanding of algebraic Morse theory's power in combinatorial algebra.

Abstract

We study how powerful algebraic discrete Morse theory is when applied to hull resolutions. The main result describes all cases when the hull resolution of the edge ideal of the complement of a triangle-free graph can be made minimal using algebraic discrete Morse theory.