Abstract by Vanessa Rico
Coloring the Map of Utah
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,r) be the number of ways to color a graph G with r colors. p(G,r) 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 graph of the map of the counties of Utah. The four of us have done that in this project.
I will begin the presentation with introducing the definition of a graph and show examples. From the examples we will explain what a planar graph is and present the graph of the counties of Utah.