Böttcher, Julia, Pruessmann, Klaas P., Taraz, Anusch and Würfl, Andreas
(2008)
*Bandwidth, treewidth, separators, expansion, and universality.*
Electronic Notes in Discrete Mathematics, 31.
pp. 91-96.
ISSN 1571-0653

## Abstract

We prove that planar graphs with bounded maximum degree have sublinear bandwidth. As a consequence for each γ>0 every n-vertex graph with minimum degree (3/4+γ)n source contains a copy of every bounded-degree planar graph on n vertices. The proof relies on the fact that planar graphs have small separators. Indeed, we show more generally that for any class of bounded-degree graphs the concepts of sublinear bandwidth, sublinear treewidth, the absence of big expanders as subgraphs, and the existence of small separators are equivalent.

Item Type: | Article |
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Official URL: | http://www.elsevier.com/wps/find/journaldescriptio... |

Additional Information: | © 2008 Elsevier B.V. |

Divisions: | Mathematics |

Subjects: | Q Science > QA Mathematics |

Sets: | Departments > Mathematics |

Date Deposited: | 28 May 2012 15:38 |

Last Modified: | 20 Feb 2021 04:14 |

URI: | http://eprints.lse.ac.uk/id/eprint/44111 |

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