Revisiting a Nice Cycle Lemma and its Consequences
Michael O. Albertson, Joan P. Hutchinson, R. Bruce Richter · arXiv (Cornell University) · 2016
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.