𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Bounds for the harmonious chromatic number of a graph

✍ Scribed by I. Krasikov; Y. Roditty

Publisher
John Wiley and Sons
Year
1994
Tongue
English
Weight
231 KB
Volume
18
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 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 Theory, 1989, pp. 291–298) are improved.

πŸ“œ SIMILAR VOLUMES

An upper bound for the harmonious chroma
An upper bound for the harmonious chromatic number of a graph
✍ 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

On an upper bound for the harmonious chr
On an upper bound for the harmonious chromatic number of a graph
✍ Zhikang Lu πŸ“‚ Article πŸ“… 1991 πŸ› John Wiley and Sons 🌐 English βš– 125 KB πŸ‘ 1 views

## 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.

Improved bounds for the chromatic number
Improved bounds for the chromatic number of a graph
✍ S. Louis Hakimi; Edward Schmeichel πŸ“‚ Article πŸ“… 2004 πŸ› John Wiley and Sons 🌐 English βš– 97 KB πŸ‘ 1 views

## Abstract After giving a new proof of a well‐known theorem of Dirac on critical graphs, we discuss the elegant upper bounds of Matula and Szekeres‐Wilf which follow from it. In order to improve these bounds, we consider the following fundamental coloring problem: given an edge‐cut (__V__~1~, __V_

A new upper bound for the harmonious chr
A new upper bound for the harmonious chromatic number
✍ 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

New bounds for the chromatic number of g
New bounds for the chromatic number of graphs
✍ Manouchehr Zaker πŸ“‚ Article πŸ“… 2008 πŸ› John Wiley and Sons 🌐 English βš– 184 KB πŸ‘ 1 views

## 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