  Let G be a combinatorial graph with vertices V and edges E. A proper coloring
of G is an assignment of colors to the vertices such that no edge connects two
vertices of the same color. These are the colorings considered in the famous
Four Color Theorem. It turns out that the number of proper colorings of G using
t colors is a polynomial in t, called the chromatic polynomial of G. This
polynomial has many wonderful properties. It also has the surprising habit of
appearing in contexts which, a priori, have nothing to do with graph coloring.
We will survey three such instances involving acyclic orientations, hyperplane
arrangements, and increasing forests. In addition, connections to symmetric
functions and algebraic geometry will be mentioned.
