Abstract by Vanessa Rico
Coloring Geographic Maps Part 1
The “Four Color Theorem” asserts that any planar graph is four colorableーmeaning four colors are sufficient to properly color any planar graph. Let P(G,t) be the polynomial describing the number of ways to color a graph G with t colors. It’s known that P(G,t) is a monic polynomial of degree |V(G)| with integer coefficients and is called the chromatic polynomial. It is surprising that no one has computed this polynomial for real-world graphs, like the map of the counties of Utah or the map of the lower 48 United States. So, in this project, we have done that.
Summary from last year’s research and major points in graph theory. Explain the chromatic polynomial for the counties of Utah.