Events

Abstract: The Map Color Theorem is a fundamental result in topological graph theory that gives a formula for the maximum number of colors needed to color a map of countries on a given surface. The most complicated part of the proof is so-called "Case 0," which concerns computing the minimum-genus surfaces that the complete graphs on 12n vertices embed in. Previous solutions of this case were complicated, where the simplest proof due to Terry et al. relies on advanced tools from abstract algebra. The purpose of this talk is to highlight a recent result that is significantly easier than all aforementioned constructions. We present a simple family of symmetric embeddings modifiable into triangular embeddings of the aforementioned complete graphs. No knowledge of graph theory or topology will be assumed.