The harmonious chromatic number of almost all trees

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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 (*) 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 languageEnglish
    Pages (from-to)31-46
    Number of pages16
    JournalCombinatorics, Probability and Computing
    Volume4
    Issue number1
    DOIs
    Publication statusPublished - 1995

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