(

graph theory):

An *orientation* of an undirected graph is an assignment of a direction to each edge. Formally, an orientation is a function `f:E->V`, where `E` is the edge set of the graph and `V` is the vertex set of the graph, such that every edge is mapped to a vertex to which it is incident. This changes an undirected graph into a directed graph (a digraph).

An acyclic orientation is an orientation which has no cycles - that is, no path on the graph can end up where it started if it must follow the edge directions. The number of acyclic orientations of a graph is given by evaluating the chromatic polynomial of the graph at `x = -1`. [Stanley, 1978]

An example of a cyclic (i.e. *not* acyclic) orientation of C_{4} is:

*-->---*
| |
^ v
| |
*--<---*