Achromatic number of collections of paths and cycles

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    A complete colouring of a simple graph G is a proper vertex colouring such that each pair of colours appears together on at least one edge. The achromatic number ?(G) is the greatest number of colours in such a colouring.
    We give simple necessary and sufficient conditions for a graph of maximum degree 2 to have a complete colouring with k colours, provided the graph is large enough, and use this to give the achromatic number for such a graph.
    Original languageEnglish
    Pages (from-to)1856–1860
    Number of pages5
    JournalDiscrete Mathematics
    Issue number19
    Publication statusPublished - 6 Oct 2013


    • Achromatic number
    • Cycles
    • Paths


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