Number of acyclic orientations

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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.

 

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