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Abstract: We establish relations between the bandwidth and the treewidth of boundeddegree graphs G, and relate these parameters to the size of a separator of G aswell as the size of an expanding subgraph of G. Our results imply that if oneof these parameters is sublinear in the number of vertices of G then so are allthe others. This implies for example that graphs of fixed genus have sublinearbandwidth or, more generally, a corresponding result for graphs with any fixedforbidden minor. As a consequence we establish a simple criterion foruniversality for such classes of graphs and show for example that for eachgamma>0 every n-vertex graph with minimum degree 3-4+gamman contains a copyof every bounded-degree planar graph on n vertices if n is sufficiently large.



Author: Julia Böttcher, Klaas P. Pruessmann, Anusch Taraz, Andreas Würfl

Source: https://arxiv.org/







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