2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/230498In this article we define a minor relation, which is stronger than the classical one, but too strong to become a well-quasi-order on the class of finite graphs. Nevertheless, with this terminology we are able to introduce a conjecture, which would imply the Lovasz conjecture and give an interesting insight on the symmetry of vertex-transitive graphs, if true. Though it could become an approach to solve the Lovasz conjecture. These ideas were first introduced by the author in his Diploma Thesis.5 pages, corrected typosCombinatoricstext