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