## 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
An upper bound for the total chromatic number
β Scribed by H. R. Hind
- Book ID
- 105309179
- Publisher
- Springer Japan
- Year
- 1990
- Tongue
- English
- Weight
- 379 KB
- Volume
- 6
- Category
- Article
- ISSN
- 0911-0119
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
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
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 that has been given by SinβMin Lee and John Mitchem is improved.