Paper by Erik D. Demaine

Reference:
Erik D. Demaine and MohammadTaghi Hajiaghayi, “Linearity of Grid Minors in Treewidth with Applications through Bidimensionality”, Combinatorica, volume 28, number 1, January 2008, pages 19–36.

Abstract:
We prove that any H-minor-free 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 H-minor-free graphs have large treewidth, up to constant factors. This strong relationship was previously known for the special cases of planar graphs and bounded-genus 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 H-minor-free graphs for any fixed H. Our result has many combinatorial consequences on bidimensionality theory, parameter-treewidth bounds, separator theorems, and bounded local treewidth; each of these combinatorial results has several algorithmic consequences including subexponential fixed-parameter algorithms and approximation algorithms.

Comments:
This paper is also available from SpringerLink.

Length:
The paper is 13 pages.

Availability:
The paper is available in PostScript (429k), gzipped PostScript (181k), and PDF (254k).
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Related papers:
GridMinors_SODA2005 (Graphs Excluding a Fixed Minor have Grids as Large as Treewidth, with Combinatorial and Algorithmic Applications through Bidimensionality)


See also other papers by Erik Demaine.
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Last updated August 14, 2014 by Erik Demaine.