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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Abstract
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.
Metadata
| 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 |
| URI: | https://eprints.bbk.ac.uk/id/eprint/24753 |
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