An acyclic orientation of an undirected graph is an orientation of its edges such that the resulting directed graph contains no cycles. The random graph G is a n, p probability space consisting of subgraphs of K that are obtained by selecting each n K -edge with independent probability p. The random
Generating the Acyclic Orientations of a Graph
β Scribed by Matthew B Squire
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 206 KB
- Volume
- 26
- Category
- Article
- ISSN
- 0196-6774
No coin nor oath required. For personal study only.
β¦ Synopsis
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 Ε½ . require O n time per acyclic orientation generated. This is the most efficient algorithm known for generating acyclic orientations.
π SIMILAR VOLUMES
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
The oriented chromatic number Ο o ( G) of an oriented graph G = (V, A) is the minimum number of vertices in an oriented graph H for which there exists a homomorphism of G to H. The oriented chromatic number Ο o (G) of an undirected graph G is the maximum of the oriented chromatic numbers of all the
A relational structure A satisfies the P(n, k) property if whenever the vertex set of A is partitioned into n nonempty parts, the substructure induced by the union of some k of the parts is isomorphic to A. The P(2, 1) property is just the pigeonhole property, (P), introduced by Cameron, and studied
## Abstract The __r__βacyclic edge chromatic number of a graph is defined to be the minimum number of colors required to produce an edge coloring of the graph such that adjacent edges receive different colors and every cycle __C__ has at least min(|__C__|, __r__) colors. We show that (__r__βββ2)__d
## Abstract A proper vertex coloring of a graph __G__β=β (__V,E__) is acyclic if __G__ contains no bicolored cycle. A graph __G__ is __L__βlist colorable if for a given list assignment __L__β=β{L(__v__): __v__ββ __V__}, there exists a proper coloring __c__ of __G__ such that __c__ (__v__)βββ__L__(_