## § The chromatic polynomial (WIP)

I've been on a combinatorics binge lately, so I'm collecting cool facts about the chromatic polynomial. We first define the chromatic function of a graph, which is a generating function:
$f[G](x) \equiv \texttt{number of ways to color G with x colors} \cdot x^n$
If we have a single vertex $K_1$, then $f[K_1](x) = n x^n$, since we can color the single vertex with the $n$ colors we have.