English

Revisiting a Nice Cycle Lemma and its Consequences

Combinatorics 2016-05-10 v3

Abstract

We correct some errors and omissions primarily in a paper [Albertson&Hutchinson2004], discovered by R.B. Richter, and also some in a proof of [Thomassen1993] and of [Yu1997]. We give a short proof of Thomassen's theorem that every triangulation of a surface with all noncontractible cycles sufficiently long can be 5-colored; part of the shortness is due to the use of the Four Color Theorem, which is not used in Thomassen's original proof.

Keywords

Cite

@article{arxiv.1602.06985,
  title  = {Revisiting a Nice Cycle Lemma and its Consequences},
  author = {M. O. Albertson and J. P. Hutchinson and R. B. Richter},
  journal= {arXiv preprint arXiv:1602.06985},
  year   = {2016}
}

Comments

9 pages

R2 v1 2026-06-22T12:55:34.118Z