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
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.
|Additional Information:||© 2009 Elsevier Ltd.|
|Library of Congress subject classification:||Q Science > QA Mathematics|
|Sets:||Departments > Mathematics|
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