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  • Clustered colouring of graph products [Elektronski vir]
    Campbell, Rutger ...
    A colouring of a graph ▫$G$▫ has clustering ▫$k$▫ if the maximum number of vertices in a monochromatic component equals ▫$k$▫. Motivated by recent results showing that many natural graph classes are ... subgraphs of the strong product of a graph with bounded treewidth and a path, this paper studies clustered colouring of strong products of two bounded treewidth graphs, where none, one, or both graphs have bounded degree. For example, in the case of two colours, if n is the number of vertices in the product, then we show that clustering ▫$\Theta(n^{2/3})$▫ is best possible, even if one of the graphs is a path. However, if both graphs have bounded degree, then clustering ▫$\Theta(n^{1/2})$▫ is best possible. With three colours, if one of the graphs has bounded degree, then we show that clustering ▫$\Theta(n^{3/7})$▫ is best possible. However, if neither graph has bounded degree, then clustering ▫$\Omega(n^{1/2})$▫ is necessary. More general bounds for any given number of colours are also presented.
    Vir: The Electronic journal of combinatorics [Elektronski vir]. - ISSN 1077-8926 (Vol. 32, iss. 3, article no. P3.15, 2025, 24 str.)
    Vrsta gradiva - e-članek ; neleposlovje za odrasle
    Leto - 2025
    Jezik - angleški
    COBISS.SI-ID - 253497859

    Povezava(-e):

    https://www.combinatorics.org/ojs/index.php/eljc/article/view/v32i3p15
    Repozitorij Univerze v Ljubljani – RUL
    DOI

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