# Upper bounds on the graph minor theorem

## TL;DR

This paper discusses recent progress in establishing upper bounds for the proof-theoretic strength of the graph minor theorem and related theorems, complementing decades of known lower bounds.

## Contribution

It presents newly found upper bounds on the graph minor theorem and explores potential improvements on existing lower bounds.

## Key findings

- Established new upper bounds for the graph minor theorem
- Provided insights into improving lower bounds for related theorems
- Enhanced understanding of the proof-theoretic strength of graph minor theorems

## Abstract

Lower bounds on the proof-theoretic strength of the graph minor theorem were found over 30 years ago by Friedman, Robertson and Seymour 1987, but upper bounds have always been elusive. We present recently found upper bounds on the graph minor theorem and other theorems appearing in the Graph Minors series. Further, we give some ideas as to how the lower bounds on some of these theorems might be improved.