# The minimal cellular resolutions of the edge ideals of forests

## TL;DR

This paper introduces an explicit minimal cellular resolution for edge ideals of forests using discrete Morse theory, simplifying the computation of algebraic invariants like Betti numbers.

## Contribution

It provides a novel construction of minimal cellular resolutions for forest edge ideals, improving computational efficiency over previous methods.

## Key findings

- Simplifies the calculation of graded Betti numbers.
- Eases the determination of projective dimension.
- Connects cellular resolutions with Lyubeznik resolution.

## Abstract

We present an explicit construction of a minimal cellular resolution for the edge ideals of forests, based on discrete Morse theory. In particular, the generators of the free modules are subsets of the generators of the modules in the Lyubeznik resolution. This procedure allows to ease the computation of the graded Betti numbers and the projective dimension.