Böttcher, Julia 
ORCID: 0000-0002-4104-3635, 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 |
|---|---|
| Official URL: | http://www.elsevier.com/wps/find/journaldescriptio... |
| Additional Information: | © 2008 Elsevier B.V. |
| Divisions: | Mathematics |
| Subjects: | Q Science > QA Mathematics |
| Date Deposited: | 28 May 2012 15:38 |
| Last Modified: | 11 Sep 2025 07:29 |
| URI: | http://eprints.lse.ac.uk/id/eprint/44111 |
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