Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-26T16:37:56.475Z Has data issue: false hasContentIssue false
  • English
  • Français

THE HARMONIOUS CHROMATIC NUMBER OF BOUNDED DEGREE GRAPHS

Published online by Cambridge University Press:  01 June 1997

KEITH EDWARDS
KEITH EDWARDS
Affiliation:
Department of Mathematics and Computer Science, University of Dundee, Dundee DD1 4HN
Get access

Abstract

A harmonious colouring of a simple graph G is a proper vertex colouring such that each pair of colours appears together on at most one edge. The harmonious chromatic number h(G) is the least number of colours in such a colouring.

Let d be a fixed positive integer, and ε>0. We show that there is a natural number M such that if G is any graph with m[ges ]M edges and maximum degree at most d, then the harmonious chromatic number h(G) satisfies

formula here

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 55 , Issue 3 , June 1997 , pp. 435 - 447
Copyright
The London Mathematical Society 1997

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)