## Number of acyclic orientations

**How many acyclic orientations are there?**

**Different acyclic orientations**

** **

Not too many people know that an acyclic orientation of an undirected graph is an assignment of a direction to each edge that does not form any directed cycle and therefore makes it into a directed acyclic graph. Keep in mind that the number of acyclic orientations may be counted using a different polynomial, the chromatic polynomial . The main idea is that there are different acyclic orientations. The main idea is that all acyclic orientations may be obtained by placing the vertices into a sequence, and then directing each edge from the earlier of its endpoints in the sequence to the later endpoint.

This fact is verified on : December 11, 2013.