The four-color theorem is a beautiful fact in math, showing that any political map can be colored in such a way that no two countries that share a border have the same color with only four colors. However, it may surprise you to learn this property is not often used in creating maps of countries. This talk will give an introduction to empire coloring — the reasons why many political maps may exceed the four-color threshold — and prove theorems about the required number of colors for some interesting maps which have qualities that are not represented in the four-color theorem.
