Sinks in Acyclic Orientations of Graphs

Details Sinks in Acyclic Orientations of Graphs Sinks in Acyclic Orientations of Graphs

1999-07-12

arxiv.org/abs/math/9907078v1

J. Combin. Theory (B) 80 (2000) 130-146

Mathematics

Combinatorics

17 pages, 1 figure

Scientific paper

Greene and Zaslavsky proved that the number of acyclic orientations of a
graph with a unique sink is, up to sign, the linear coefficient of the
chromatic polynomial. We give three new proofs of this result using pure
induction, noncommutative symmetric functions, and an algorithmic bijection.

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