Harmonious chromatic number of directed graphs

    Research output: Contribution to journalArticle

    5 Citations (Scopus)

    Abstract

    We consider the extension to directed graphs of the concepts of harmonious colouring and complete colouring. We give an upper bound for the harmonious chromatic number of a general directed graph, and show that determining the exact value of the harmonious chromatic number is NP-hard for directed graphs of bounded degree (in fact graphs with maximum indegree and outdegree 2); the complexity of the corresponding undirected case is not known. We also consider complete colourings, and show that in the directed case the existence of a complete colouring is NP-complete. We also show that the interpolation property for complete colourings fails in the directed case.
    Original languageEnglish
    Pages (from-to)369-376
    Number of pages8
    JournalDiscrete Applied Mathematics
    Volume161
    Issue number3
    DOIs
    Publication statusPublished - 2013

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    Directed graphs
    Coloring
    Chromatic number
    Directed Graph
    Colouring
    NP-complete problem
    Interpolation
    Interpolate
    Upper bound
    Graph in graph theory

    Cite this

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    abstract = "We consider the extension to directed graphs of the concepts of harmonious colouring and complete colouring. We give an upper bound for the harmonious chromatic number of a general directed graph, and show that determining the exact value of the harmonious chromatic number is NP-hard for directed graphs of bounded degree (in fact graphs with maximum indegree and outdegree 2); the complexity of the corresponding undirected case is not known. We also consider complete colourings, and show that in the directed case the existence of a complete colouring is NP-complete. We also show that the interpolation property for complete colourings fails in the directed case.",
    author = "Edwards, {Keith J.}",
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    language = "English",
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    Harmonious chromatic number of directed graphs. / Edwards, Keith J.

    In: Discrete Applied Mathematics, Vol. 161, No. 3, 2013, p. 369-376.

    Research output: Contribution to journalArticle

    TY - JOUR

    T1 - Harmonious chromatic number of directed graphs

    AU - Edwards, Keith J.

    N1 - Copyright 2012 Elsevier B.V., All rights reserved.

    PY - 2013

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    N2 - We consider the extension to directed graphs of the concepts of harmonious colouring and complete colouring. We give an upper bound for the harmonious chromatic number of a general directed graph, and show that determining the exact value of the harmonious chromatic number is NP-hard for directed graphs of bounded degree (in fact graphs with maximum indegree and outdegree 2); the complexity of the corresponding undirected case is not known. We also consider complete colourings, and show that in the directed case the existence of a complete colouring is NP-complete. We also show that the interpolation property for complete colourings fails in the directed case.

    AB - We consider the extension to directed graphs of the concepts of harmonious colouring and complete colouring. We give an upper bound for the harmonious chromatic number of a general directed graph, and show that determining the exact value of the harmonious chromatic number is NP-hard for directed graphs of bounded degree (in fact graphs with maximum indegree and outdegree 2); the complexity of the corresponding undirected case is not known. We also consider complete colourings, and show that in the directed case the existence of a complete colouring is NP-complete. We also show that the interpolation property for complete colourings fails in the directed case.

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    DO - 10.1016/j.dam.2012.09.003

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