2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/231032The better title is "Yet another FALSE proof of the 4-colour theorem." Please consider all versions of this paper as historical material on the way to a non-computer proof of the 4-colour theorem. Interpreted as proofs, all versions are wrong.This paper has been withdrawnGeneral Mathematics05C15Yet another short proof of the 4-colour theoremtext