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
On an upper bound for the harmonious chromatic number of a graph
β Scribed by Zhikang Lu
- Publisher
- John Wiley and Sons
- Year
- 1991
- Tongue
- English
- Weight
- 125 KB
- Volume
- 15
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
β¦ Synopsis
Abstract
The upper bound for the harmonious chromatic number of a graph that has been given by SinβMin Lee and John Mitchem is improved.
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
## 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
## Abstract In this paper we consider those graphs that have maximum degree at least 1/__k__ times their order, where __k__ is a (small) positive integer. A result of Hajnal and SzemerΓ©di concerning equitable vertexβcolorings and an adaptation of the standard proof of Vizing's Theorem are used to s
In 1968, Vizing conjectured that if G is a -critical graph with n vertices, then (G) β€ n / 2, where (G) is the independence number of G. In this paper, we apply Vizing and Vizing-like adjacency lemmas to this problem and prove that (G)<(((5 -6)n) / (8 -6))<5n / 8 if β₯ 6. α§ 2010 Wiley