Greene and Zaslavsky proved that the number of acyclic orientations of a graph G with a unique sink at a given vertex is, up to sign, the linear coefficient of the chromatic polynomial. We give three proofs of this result using pure induction, noncommutative symmetric functions, and an algorithmic b
Determination of the paths in an oriented acyclical graph
โ Scribed by S. I. Garkavenko; L. S. Berdnikova
- Publisher
- Springer US
- Year
- 1980
- Tongue
- English
- Weight
- 381 KB
- Volume
- 15
- Category
- Article
- ISSN
- 1573-8337
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The acyclic orientation graph, AO(G), of an undirected graph, G, is the graph whose vertices are the acyclic orientations of G and whose edges are the pairs of orientations differing only by the reversal of one edge. Edelman (1984) has observed that it follows from results on polytopes that when G i
The acyclic orientations of a graph are related to its chromatic polynomial, to its reliability, and to certain hyperplane arrangements. In this paper, an algorithm for listing the acyclic orientations of a graph is presented. The algorithm is shown to ลฝ . require O n time per acyclic orientation ge