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
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.
|Additional Information:||© 2008 Elsevier B.V.|
|Library of Congress subject classification:||Q Science > QA Mathematics|
|Sets:||Departments > Mathematics|
|Date Deposited:||28 May 2012 15:38|
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