Paper by Erik D. Demaine
- 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.
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.
- The paper is 8 pages.
- The paper is available in PostScript (286k), gzipped PostScript (101k), and PDF (160k).
- See information on file formats.
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- Related papers:
- GridMinors_Combinatorica (Linearity of Grid Minors in Treewidth with Applications through Bidimensionality)
See also other papers by Erik Demaine.
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