English

A shorter proof of the path-width theorem

Combinatorics 2023-09-12 v1

Abstract

A graph has {\em path-width} at most ww if it can be built from a sequence of graphs each with at most w+1w+1 vertices, by overlapping consecutive terms. Every graph with path-width at least w1w-1 contains every ww-vertex forest as a minor: this was originally proved by Bienstock, Robertson, Thomas and the author, and was given a short proof by Diestel. Here we give a proof even shorter and simpler than that of Diestel.

Keywords

Cite

@article{arxiv.2309.05100,
  title  = {A shorter proof of the path-width theorem},
  author = {P. Seymour},
  journal= {arXiv preprint arXiv:2309.05100},
  year   = {2023}
}
R2 v1 2026-06-28T12:17:28.372Z