English

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

Combinatorics 2021-02-04 v4 Discrete Mathematics

Abstract

We prove the conjecture of Seymour (1993) that for every apex-forest H1H_1 and outerplanar graph H2H_2 there is an integer pp such that every 2-connected graph of pathwidth at least pp contains H1H_1 or H2H_2 as a minor. An independent proof was recently obtained by Dang and Thomas.

Keywords

Cite

@article{arxiv.1801.01833,
  title  = {Seymour's conjecture on 2-connected graphs of large pathwidth},
  author = {Tony Huynh and Gwenaël Joret and Piotr Micek and David R. Wood},
  journal= {arXiv preprint arXiv:1801.01833},
  year   = {2021}
}

Comments

v4: Small changes suggested by a referee

R2 v1 2026-06-22T23:37:36.789Z