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Bandwidth, expansion, treewidth, separators and universality for bounded-degree graphs

Böttcher, Julia, 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

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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
Official URL: http://www.journals.elsevier.com/european-journal-...
Additional Information: © 2009 Elsevier Ltd.
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 15:19
URL: http://eprints.lse.ac.uk/44106/

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