In 1968, Vizing conjectured that if G is a -critical graph with n vertices, then (G) โค 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 โฅ 6. แญง 2010 Wiley
Upper bounds for the 2-hued chromatic number of graphs in terms of the independence number
โ Scribed by A. Dehghan; A. Ahadi
- Book ID
- 116401278
- Publisher
- Elsevier Science
- Year
- 2012
- Tongue
- English
- Weight
- 203 KB
- Volume
- 160
- Category
- Article
- ISSN
- 0166-218X
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## Abstract In this article we first give an upper bound for the chromatic number of a graph in terms of its degrees. This bound generalizes and modifies the bound given in 11. Next, we obtain an upper bound of the order of magnitude ${\cal O}({n}^{{1}-\epsilon})$ for the coloring number of a graph
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