\indent given a fixed graph $g$ on $n$ vertices, we can create a random coloring of $g$ in the following way: randomly pick an edge, then randomly pick a color, and then color both endpoints of that edge that color. we can continue this process on a graph that is already colored by simply overwriting any vertices that have already been assigned a color. this gives rise to a random walk on the $2^n$ colorings of $g$, and it is this random walk that we will investigate. the eigenvalues of the transition matrix are known and have a simple form. we discuss these and other quantities as well as several related problems.