𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On an upper bound for the harmonious chromatic number of a graph

✍ 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.

✦ Synopsis


Abstract

The upper bound for the harmonious chromatic number of a graph that has been given by Sin‐Min Lee and John Mitchem is improved.


πŸ“œ SIMILAR VOLUMES


An upper bound for the harmonious chroma
✍ Sin-Min Lee; John Mitchem πŸ“‚ Article πŸ“… 1987 πŸ› John Wiley and Sons 🌐 English βš– 149 KB πŸ‘ 1 views

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 new upper bound for the harmonious chr
✍ Edwards, Keith πŸ“‚ Article πŸ“… 1998 πŸ› John Wiley and Sons 🌐 English βš– 200 KB πŸ‘ 2 views

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

Bounds for the harmonious chromatic numb
✍ I. Krasikov; Y. Roditty πŸ“‚ Article πŸ“… 1994 πŸ› John Wiley and Sons 🌐 English βš– 231 KB πŸ‘ 2 views

## 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. 345–347 and 629–636) and the lower bound given by D. G. Beane, N. L. Biggs, and B. J. Wilson (__Journal of Graph T

An upper bound for the total chromatic n
✍ H. R. Hind πŸ“‚ Article πŸ“… 1992 πŸ› John Wiley and Sons 🌐 English βš– 340 KB πŸ‘ 1 views

## 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 vertex‐colorings and an adaptation of the standard proof of Vizing's Theorem are used to s

A new upper bound for the independence n
✍ Rong Luo; Yue Zhao πŸ“‚ Article πŸ“… 2010 πŸ› John Wiley and Sons 🌐 English βš– 107 KB πŸ‘ 1 views

In 1968, Vizing conjectured that if G is a -critical graph with n vertices, then (G) ≀ 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