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SODA
2016
ACM

An Algorithmic Hypergraph Regularity Lemma

7 years 11 months ago
An Algorithmic Hypergraph Regularity Lemma
Szemer´edi’s Regularity Lemma [22, 23] is one of the most powerful tools in combinatorics. It asserts that all large graphs G admit a bounded partition of E(G), most classes of which consist of regularly distributed edges. The original proof of this result was non-constructive. A constructive proof was given by Alon, Duke, Lefmann, R¨odl and Yuster [1], which allows one to efficiently construct a regular partition for any large graph. Szemer´edi’s Regularity Lemma was extended to hypergraphs by various authors. Frankl and R¨odl [3] gave one such extension to 3-uniform hypergraphs, and R¨odl and Skokan [19] extended this result to k-uniform hypergraphs. W.T. Gowers [4, 5] gave another such extension, using a different concept of regularity than that of Frankl, R¨odl and Skokan. Similarly to the graph case, all of these proofs are non-constructive. In this paper, we report on a constructive proof of Gowers’ Hypergraph Regularity Lemma, and discuss an application.
Brendan Nagle, Vojtech Rödl, Mathias Schacht
Added 09 Apr 2016
Updated 09 Apr 2016
Type Journal
Year 2016
Where SODA
Authors Brendan Nagle, Vojtech Rödl, Mathias Schacht
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