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

Authors:
Julia Böttcher;Klaas P. Pruessmann;Anusch Taraz;Andreas Würfl
Affiliations:
Zentrum Mathematik, Technische Universität München, Boltzmannstraíe 3, D-85747 Garching bei München, Germany;Institute for Biomedical Engineering, University and ETH Zurich, Gloriastr. 35, 8092, Zürich, Switzerland;Zentrum Mathematik, Technische Universität München, Boltzmannstraíe 3, D-85747 Garching bei München, Germany;Zentrum Mathematik, Technische Universität München, Boltzmannstraíe 3, D-85747 Garching bei München, Germany
Venue:
European Journal of Combinatorics
Year:
2010

Citing 10
Cited 5

A separator theorem for graphs of bounded genus

Journal of Algorithms
Graph minors. V. Excluding a planar graph

Journal of Combinatorial Theory Series B
Universal graphs for bounded-degree trees and planar graphs

SIAM Journal on Discrete Mathematics
A partial k-arboretum of graphs with bounded treewidth

Theoretical Computer Science
The Blow-up Lemma

Combinatorics, Probability and Computing
Graph Minors. XX. Wagner's conjecture

Journal of Combinatorial Theory Series B - Special issue dedicated to professor W. T. Tutte
Large planar subgraphs in dense graphs

Journal of Combinatorial Theory Series B
Graph drawings with few slopes

Computational Geometry: Theory and Applications
Sparse universal graphs for bounded-degree graphs

Random Structures & Algorithms
On tree width, bramble size, and expansion

Journal of Combinatorial Theory Series B

Bandwidth theorem for random graphs

Journal of Combinatorial Theory Series B
Embedding into Bipartite Graphs

SIAM Journal on Discrete Mathematics
Treewidth of Erdős-Rényi random graphs, random intersection graphs, and scale-free random graphs

Discrete Applied Mathematics
Finding a Periodic Attractor of a Boolean Network

IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
On prisms, Möbius ladders and the cycle space of dense graphs

European Journal of Combinatorics

Quantified Score

Hi-index	0.00

Visualization

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 @c0 every n-vertex graph with minimum degree (34+@c)n contains a copy of every bounded-degree planar graph on n vertices if n is sufficiently large.