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The Harmonious Chromatic Number of Almost All Trees

Published online by Cambridge University Press:  12 September 2008

Keith Edwards
Keith Edwards
Affiliation:
Department of Mathematics and Computer Science, University of Dundee, Dundee DD1 4HN, U.K.
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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.

For any positive integer m, let Q(m) be the least positive integer k such that ≥ m. We show that for almost all unlabelled, unrooted trees T, h(T) = Q(m), where m is the number of edges of T.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 4 , Issue 1 , March 1995 , pp. 31 - 46
Copyright
Copyright © Cambridge University Press 1995

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