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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
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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

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