Böttcher, Julia ORCID: 0000-0002-4104-3635, Pruessmann, Klaas P., Taraz, Anusch and Würfl, Andreas
(2010)
*Bandwidth, expansion, treewidth, separators and universality for bounded-degree graphs.*
European Journal of Combinatorics, 31 (5).
pp. 1217-1227.
ISSN 0195-6698

## Abstract

We establish relations between the bandwidth and the treewidth of bounded degree graphs G, and relate these parameters to the size of a separator of G as well as the size of an expanding subgraph of G. Our results imply that if one of these parameters is sublinear in the number of vertices of G then so are all the others. This implies for example that graphs of fixed genus have sublinear bandwidth or, more generally, a corresponding result for graphs with any fixed forbidden minor. As a consequence we establish a simple criterion for universality for such classes of graphs and show for example that for each γ>0 every n-vertex graph with minimum degree (3/4 + γ)n contains a copy of every bounded-degree planar graph on n vertices if n is sufficiently large.

Item Type: | Article |
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Official URL: | http://www.journals.elsevier.com/european-journal-... |

Additional Information: | © 2009 Elsevier Ltd. |

Divisions: | Mathematics |

Subjects: | Q Science > QA Mathematics |

Sets: | Departments > Mathematics |

Date Deposited: | 28 May 2012 15:19 |

Last Modified: | 20 Sep 2021 00:49 |

URI: | http://eprints.lse.ac.uk/id/eprint/44106 |

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