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arXiv · 0910.3014

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

Julia Böttcher·Klaas P. Pruessmann·Anusch Taraz·Andreas Würfl
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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 gamma>0 every n-vertex graph with minimum degree ((3/4)+gamma)n contains a copy of every bounded-degree planar graph on n vertices if n is sufficiently large.

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Julia Böttcher, Klaas P. Pruessmann, Anusch Taraz, Andreas Würfl. 2009-10-16. Bandwidth, expansion, treewidth, separators, and universality for bounded degree graphs. https://arxiv.org/abs/0910.3014

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