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Journal of the London Mathematical Society 1997 55(3):435-447; doi:10.1112/S0024610797004857
© 1997 by London Mathematical Society
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© The London Mathematical Society

The Harmonious Chromatic Number of Bounded Degree Graphs

Keith Edwards

Department of Mathematics and Computer Science, University of Dundee Dundee DD1 4HN

Received 30 January 1995.

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 {varepsilon}>0. We show that there is a natural number M such that if G is any graph with m≥M edges and maximum degree at most d, then the harmonious chromatic number h(G) satisfies


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