Directed Graphs and Network Flows · Superchallenge problem

By Stanley's theorem, $|P(G,-1)|$ counts the acyclic orientations of a graph $G$. The $5$-cycle $C_5$ has chromatic polynomial $P(C_5,k) = (k-1)^5 - (k-1) = (k-1)[(k-1)^4 - 1]$. How many acyclic orientations does $C_5$ have?