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Bandwidth, treewidth, separators, expansion, and universality

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

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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.
Library of Congress subject classification: Q Science > QA Mathematics
Sets: Departments > Mathematics
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Date Deposited: 28 May 2012 15:38
URL: http://eprints.lse.ac.uk/44111/

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