## Abstract The upper bound for the harmonious chromatic number of a graph given by Zhikang Lu and by C. McDiarmid and Luo Xinhua, independently (__Journal of Graph Theory__, 1991, pp. 345β347 and 629β636) and the lower bound given by D. G. Beane, N. L. Biggs, and B. J. Wilson (__Journal of Graph T
The growth rate of the harmonious chromatic number
β Scribed by Donald G. Beane; Norman L. Biggs; Brian J. Wilson
- Publisher
- John Wiley and Sons
- Year
- 1989
- Tongue
- English
- Weight
- 419 KB
- Volume
- 13
- Category
- Article
- ISSN
- 0364-9024
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π SIMILAR VOLUMES
A harmonious coloring of a simple graph G is a proper vertex coloring such that each pair of colors appears together on at most one edge. The harmonious chromatic number h(G) is the least number of colors in such a coloring. We obtain a new upper bound for the harmonious chromatic number of general
An upper bound for the harmonious chromatic number of a graph G is given. Three corollaries of the theorem are theorems or improvements of the theorems of Miller and Pritikin. The assignment of colors to the vertices of a graph such that each vertex has exactly one color has been studied for well o
## Abstract The upper bound for the harmonious chromatic number of a graph that has been given by SinβMin Lee and John Mitchem is improved.
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
For a pair of integers 1 F β₯r, the β₯-chromatic number of an r-uniform Ε½ . hypergraph H s V, E is the minimal k, for which there exists a partition of V into subsets < < T, . . . , T such that e l T F β₯ for every e g E. In this paper we determine the asymptotic 1 k i Ε½ . behavior of the β₯-chromatic n