How many ways to color the map of America?

Abstract

Although the Four Color Conjecture originated in cartography, surprisingly, there is nothing in the literature on the number of ways to color an actual geographic map with four or fewer colors. In this paper, we compute these numbers, with exponentially increasing order of difficulty, for the maps of Canada, France, and the USA. Our attempts to compute the latter two lead to some new results on the chromatic polynomial of graphs.