Paper by Erik D. Demaine

Reference:

Erik D. Demaine and MohammadTaghi Hajiaghayi, “Bidimensionality, Map Graphs, and Grid Minors”, Manuscript, February 2005.

Abstract:

In this paper we extend the theory of bidimensionality to two families of graphs that do not exclude fixed minors: map graphs and power graphs. In both cases we prove a polynomial relation between the treewidth of a graph in the family and the size of the largest grid minor. These bounds improve the running times of a broad class of fixed-parameter algorithms. Our novel technique of using approximate max-min relations between treewidth and size of grid minors is powerful, and we show how it can also be used, e.g., to prove a linear relation between the treewidth of a bounded-genus graph and the treewidth of its dual.

Comments:

This paper is also available as arXiv:cs.DM/0502070 of the Computing Research Repository (CoRR).

Length:

The paper is 12 pages.

Availability:

The paper is available in PostScript (266k), gzipped PostScript (96k), and PDF (149k).

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