  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.

Logic;Computational Complexity