Seymour's conjecture on 2-connected graphs of large pathwidth

Abstract

We prove the conjecture of Seymour (1993) that for every apex-forest $H_1$ and outerplanar graph $H_2$ there is an integer $p$ such that every 2-connected graph of pathwidth at least $p$ contains $H_1$ or $H_2$ as a minor. An independent proof was recently obtained by Dang and Thomas.

v4: Small changes suggested by a referee