The harmonious chromatic number of bounded degree graphs

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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 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 languageEnglish
    Pages (from-to)435-447
    Number of pages13
    JournalJournal of the London Mathematical Society
    Volume55
    Issue number3
    Publication statusPublished - 1997

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