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
An upper bound for the adjacent vertex distinguishing acyclic edge chromatic number of a graph
β Scribed by Xin-sheng Liu; Ming-qiang An; Yang Gao
- Publisher
- Institute of Applied Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
- Year
- 2008
- Tongue
- English
- Weight
- 159 KB
- Volume
- 25
- Category
- Article
- ISSN
- 0168-9673
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## Abstract The upper bound for the harmonious chromatic number of a graph that has been given by SinβMin Lee and John Mitchem is improved.
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
## 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
## Abstract The path number of a graph __G__, denoted __p(G)__, is the minimum number of edgeβdisjoint paths covering the edges of __G.__ LovΓ‘sz has proved that if __G__ has __u__ odd vertices and __g__ even vertices, then __p(G)__ β€ 1/2 __u__ + __g__ β 1 β€ __n__ β 1, where __n__ is the total numbe