NDLI: Polynomial bounds for the grid-minor theorem

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Polynomial bounds for the grid-minor theorem

Content Provider	ACM Digital Library
Author	Chekuri, Chandra Chuzhoy, Julia
Abstract	One of the key results in Robertson and Seymour's seminal work on graph minors is the Grid-Minor Theorem (also called the Excluded Grid Theorem). The theorem states that for every fixed-size grid H, every graph whose treewidth is large enough, contains H as a minor. This theorem has found many applications in graph theory and algorithms. Let f(k) denote the largest value, such that every graph of treewidth k contains a grid minor of size f(k) × f(k). The best current quantitative bound, due to recent work of Kawarabayashi and Kobayashi [15], and Leaf and Seymour [18], shows that f(k) = Ω(√logk/loglogk). In contrast, the best known upper bound implies that f(k) = O(√k/logk) [22]. In this paper we obtain the first polynomial relationship between treewidth and grid-minor size by showing that f(k) = $Ω(k^{Δ})$ for some fixed constant Δ > 0, and describe an algorithm, whose running time is polynomial in \|V (G)\| and k, that finds a model of such a grid-minor in G.
Starting Page	60
Ending Page	69
Page Count	10
File Format	PDF MP4
ISBN	9781450327107
DOI	10.1145/2591796.2591813
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2014-05-31
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Grid minor theorem Treewidth
Content Type	Audio Text
Resource Type	Article

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