## Abstract A proper edge coloring of a graph __G__ is called acyclic if there is no 2βcolored cycle in __G__. The acyclic edge chromatic number of __G__, denoted by Ο(__G__), is the least number of colors in an acyclic edge coloring of __G__. In this paper, we determine completely the acyclic edge
On the Acyclic Chromatic Number of Hamming Graphs
β Scribed by Robert E. Jamison; Gretchen L. Matthews
- Publisher
- Springer Japan
- Year
- 2008
- Tongue
- English
- Weight
- 160 KB
- Volume
- 24
- Category
- Article
- ISSN
- 0911-0119
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π SIMILAR VOLUMES
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
## 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 Star chromatic number, introduced by A. Vince, is a natural generalization of chromatic number. We consider the question, βWhen is Ο\* < Ο?β We show that Ο\* < Ο if and only if a particular digraph is acyclic and that the decisioin problem associated with this question is probably not i
Colorings of disk graphs arise in the study of the frequency-assignment problem in broadcast networks. Motivated by the observations that the chromatic number of graphs modeling real networks hardly exceeds their clique number, we examine the related properties of the unit disk (UD) graphs and their