Linearity of grid minors in treewidth with applications through bidimensionality
 Erik D. Demaine,
 Mohammadtaghi Hajiaghayi
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We prove that any Hminorfree graph, for a fixed graph H, of treewidth w has an Ω(w) × Ω(w) grid graph as a minor. Thus grid minors suffice to certify that Hminorfree graphs have large treewidth, up to constant factors. This strong relationship was previously known for the special cases of planar graphs and boundedgenus graphs, and is known not to hold for general graphs. The approach of this paper can be viewed more generally as a framework for extending combinatorial results on planar graphs to hold on Hminorfree graphs for any fixed H. Our result has many combinatorial consequences on bidimensionality theory, parametertreewidth bounds, separator theorems, and bounded local treewidth; each of these combinatorial results has several algorithmic consequences including subexponential fixedparameter algorithms and approximation algorithms.
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 Title
 Linearity of grid minors in treewidth with applications through bidimensionality
 Journal

Combinatorica
Volume 28, Issue 1 , pp 1936
 Cover Date
 20080101
 DOI
 10.1007/s0049300821404
 Print ISSN
 02099683
 Online ISSN
 14396912
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 05C83
 05C85
 68R10
 Industry Sectors
 Authors

 Erik D. Demaine ^{(1)}
 Mohammadtaghi Hajiaghayi ^{(1)}
 Author Affiliations

 1. MIT, Computer Science and Artificial Intelligence Laboratory, 32 Vassar Street, Cambridge, MA, 02139, USA