# On the cover ideals of chordal graphs

## TL;DR

This paper explores the algebraic properties of cover ideals of chordal graphs, providing recursive formulas for their Betti numbers and offering new shellings of the independence complex.

## Contribution

It introduces recursive formulas for Betti numbers of cover ideals of chordal graphs and presents a new proof of shellability of the independence complex.

## Key findings

- Betti numbers of cover ideals can be computed recursively
- The independence complex of a chordal graph is shellable
- New shellings of the independence complex are provided

## Abstract

The independence complex of a chordal graph is known to be shellable due to a result of Van Tuyl and Villarreal. This is equivalent to the fact that cover ideal of a chordal graph has linear quotients. We use this result to obtain recursive formulas for the Betti numbers of cover ideals of chordal graphs. Also, we give a new proof of their result which yields different shellings of the independence complex.