Paper by Erik D. Demaine

Reference:

Erik D. Demaine and MohammadTaghi Hajiaghayi, “Graphs Excluding a Fixed Minor have Grids as Large as Treewidth, with Combinatorial and Algorithmic Applications through Bidimensionality”, in Proceedings of the 16th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2005), Vancouver, British Columbia, Canada, January 23–25, 2005, pages 682–689.

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.

Length:

The paper is 8 pages.

Availability:

The paper is available in PostScript (286k), gzipped PostScript (101k), and PDF (160k).

See information on file formats.

[Google Scholar search]

Related papers:

GridMinors_Combinatorica (Linearity of Grid Minors in Treewidth with Applications through Bidimensionality)