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An exploration of proofs of the Szemerédi regularity lemma


Abstract This paper focuses on the Szemerédi regularity lemma, a result in the field of extremal graph theory. The lemma says that every graph can be partitioned into bounded equal parts such that most edges of the graph span these partitions, and these edges are distributed in a fairly uniform way. Definitions and notation will be established, leading to explorations of three proofs of the regularity lemma. These are a version of the original proof, a Pythagoras proof utilizing elemental geometry, and a proof utilizing concepts of spectral graph theory. This paper is intended to supplement the proofs with background information about the concepts utilized. Furthermore, it is the hope that this paper will serve as another resource for students and... (more)
Created Date 2015-05
Contributor Byrne, Michael John (Author) / Czygrinow, Andrzej (Thesis Director) / Kierstead, Hal (Committee Member) / Barrett, The Honors College / School of Mathematical and Statistical Sciences / Department of Chemistry and Biochemistry
Subject Regularity Lemma / Mathematics / Graph Theory
Series Academic Year 2014-2015
Type Text
Extent 36 pages
Language English
Copyright
Reuse Permissions All Rights Reserved
Collaborating Institutions Barrett, the Honors College
Additional Formats MODS / OAI Dublin Core / RIS


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