### 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 ot colours in such a colouring. Let d be a fixed positive integer, and e > 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 (2m) = h(G) = (1+e) (2m).

Original language | English |
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Pages (from-to) | 435-447 |

Number of pages | 13 |

Journal | Journal of the London Mathematical Society |

Volume | 55 |

Issue number | 3 |

Publication status | Published - 1997 |

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## Cite this

Edwards, K. (1997). The harmonious chromatic number of bounded degree graphs.

*Journal of the London Mathematical Society*,*55*(3), 435-447.