The harmonious chromatic number and the achromatic number

    Research output: Chapter in Book/Report/Conference proceedingChapter

    Abstract

    The harmonious chromatic number of a graph is the least number of colours in a vertex colouring such that each pair of colours appears on at most one edge. The achromatic number of a graph is the greatest number of colours in a vertex colouring such that each pair of colours appears on at least one edge. This paper is a survey of what is known about these two parameters, in particular we look at upper and lower bounds, special classes of graphs and complexity issues.
    Original languageEnglish
    Title of host publicationSurveys in combinatorics, 1997
    EditorsR. A. Bailey
    PublisherCambridge University Press
    Pages13-48
    Number of pages36
    ISBN (Electronic)9780511662119
    ISBN (Print)0521598400
    DOIs
    Publication statusPublished - 1997

    Publication series

    NameLondon Mathematical Society Lecture Note Series
    Volume241

    Fingerprint

    Achromatic number
    Chromatic number
    Vertex Coloring
    Graph in graph theory
    Two Parameters
    Upper and Lower Bounds
    Color

    Cite this

    Edwards, K. (1997). The harmonious chromatic number and the achromatic number. In R. A. Bailey (Ed.), Surveys in combinatorics, 1997 (pp. 13-48). (London Mathematical Society Lecture Note Series; Vol. 241). Cambridge University Press. https://doi.org/10.1017/CBO9780511662119.003
    Edwards, Keith. / The harmonious chromatic number and the achromatic number. Surveys in combinatorics, 1997. editor / R. A. Bailey. Cambridge University Press, 1997. pp. 13-48 (London Mathematical Society Lecture Note Series).
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    Edwards, K 1997, The harmonious chromatic number and the achromatic number. in RA Bailey (ed.), Surveys in combinatorics, 1997. London Mathematical Society Lecture Note Series, vol. 241, Cambridge University Press, pp. 13-48. https://doi.org/10.1017/CBO9780511662119.003

    The harmonious chromatic number and the achromatic number. / Edwards, Keith.

    Surveys in combinatorics, 1997. ed. / R. A. Bailey. Cambridge University Press, 1997. p. 13-48 (London Mathematical Society Lecture Note Series; Vol. 241).

    Research output: Chapter in Book/Report/Conference proceedingChapter

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    Edwards K. The harmonious chromatic number and the achromatic number. In Bailey RA, editor, Surveys in combinatorics, 1997. Cambridge University Press. 1997. p. 13-48. (London Mathematical Society Lecture Note Series). https://doi.org/10.1017/CBO9780511662119.003