## 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 (*) S: m. We show that for almost all unlabelled, unrooted trees T, h(T) = Q(m), where m is the number of edges of T.

Copyright © Cambridge University Press 1995

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

Copyright © Cambridge University Press 1995

Original language | English |
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Pages (from-to) | 31-46 |

Number of pages | 16 |

Journal | Combinatorics, Probability and Computing |

Volume | 4 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1995 |