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    Characterising bounded expansion by neighbourhood complexity

    Reidl, Felix and Sánchez Villaamil, F. and Stavropoulos, K. (2018) Characterising bounded expansion by neighbourhood complexity. European Journal of Combinatorics 75 , pp. 152-168. ISSN 0195-6698.

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    We show that a graph class $\cal G$ has \emph{bounded expansion} if and only if it has bounded \emph{$r$-neighbourhood complexity}, \ie for any vertex set $X$ of any subgraph~$H$ of any $G\in\cal G$, the number of subsets of $X$ which are exact $r$-neighbourhoods of vertices of $H$ on $X$ is linear in the size of $X$. This is established by bounding the $r$-neighbourhood complexity of a graph in terms of both its \emph{$r$-centred colouring number} and its \emph{weak $r$-colouring number}, which provide known characterisations to the property of bounded expansion.


    Item Type: Article
    School: Birkbeck Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences
    Depositing User: Felix Reidl
    Date Deposited: 26 Oct 2018 07:04
    Last Modified: 09 Aug 2023 12:45


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