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
On the chromatic number of the product of graphs
β Scribed by D. Duffus; B. Sands; R. E. Woodrow
- Publisher
- John Wiley and Sons
- Year
- 1985
- Tongue
- English
- Weight
- 429 KB
- Volume
- 9
- Category
- Article
- ISSN
- 0364-9024
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π SIMILAR VOLUMES
We introduce in this paper the notion of the chromatic number of an oriented graph G (that is of an antisymmetric directed graph) defined as the minimum order of an oriented graph H such that G admits a homomorphism to H. We study the chromatic number of oriented k-trees and of oriented graphs with
## Abstract This article studies the circular chromatic number of a class of circular partitionable graphs. We prove that an infinite family of circular partitionable graphs __G__ has $\chi\_ c (G) = \chi(G)$. A consequence of this result is that we obtain an infinite family of graphs __G__ with th
The star-chromatic number of a graph, a parameter introduced by Vince, is a natural generalization of the chromatic number of a graph. Here we construct planar graphs with star-chromatic number r, where r is any rational number between 2 and 3, partially answering a question of Vince.
## Abstract The fractional chromatic number of a graph __G__ is the infimum of the total weight that can be assigned to the independent sets of __G__ in such a way that, for each vertex __v__ of __G__, the sum of the weights of the independent sets containing __v__ is at least 1. In this note we g