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Acyclic Orientation


An acyclic orientation of an undirected graph is a graph orientation that has no directed cycles, so the resulting directed graph is an acyclic digraph (Stanley 1973).

For a finite graph G with n vertices and chromatic polynomial pi_G(t), the number of acyclic orientations is (-1)^npi_G(-1) (Stanley 1973).


See also

Acyclic Digraph, Chromatic Polynomial, Graph Orientation

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References

Stanley, R. P. "Acyclic Orientations of Graphs." Disc. Math. 5, 171-178, 1973. https://doi.org/10.1016/0012-365X(73)90108-8.

Cite this as:

Weisstein, Eric W. "Acyclic Orientation." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/AcyclicOrientation.html

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