A Search of The Four-Color Theorem and its Higher Dimensional Generalization

摘要

Four-Color Theorem has secret in its logical proof and actual operating. Inthis paper we will give a proof of Four-Color Theorem based on Kuratowski'sTheorem using some induction argument and give a description of the mostcomplicated coloring map, a simple proof of Kuratowski's Theorem using Eulercharateristic is also presented. We also conjecture the higher dimensionalgeneralization of Four-Color Theorem.