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Stability results in additive combinatorics and graph theory
Descriptive
TitleInfo
Title
Stability results in additive combinatorics and graph theory
Name
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NamePart
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Herdade
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(type = given)
Simao
NamePart
(type = date)
1984-
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Simao Herdade
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author
Name
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Szemerédi
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Endre
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Endre Szemerédi
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Advisory Committee
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chair
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Komlós
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János
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János Komlós
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Advisory Committee
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internal member
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Steiger
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William
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William Steiger
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Advisory Committee
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internal member
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Magyar
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Ákos
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Ákos Magyar
Affiliation
Advisory Committee
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outside member
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Rutgers University
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degree grantor
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Graduate School - New Brunswick
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school
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Text
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theses
OriginInfo
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2015
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2015-05
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2015
Place
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xx
Language
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eng
Abstract
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A general problem in Extremal Combinatorics asks about the maximum size of a collection of finite objects satisfying certain restrictions, and an ideal solution to it presents to you the objects which attain the maximum size. In several problems, it is the case that any large set satisfying the given property must be similar to one of the few extremal examples. Such stability results give us a complete understanding of the problem, and also make the result more flexible to be applied as a tool in other mathematical problems. Stability results in additive combinatorics and graph theory constitute the main topic of this thesis, in which we solve a question of Erdös and Sarközy on sums of integers, and reprove a conjecture of Posa and Seymour on powers of hamiltonian cycles. Along the way we prove stronger structural statements that have as a corollary the optimal solution to these problems. We also introduce a counting technique and two graph theory tools which we believe to be of great interest in their own right. Namely the Shifting Method, the Connecting Lemma, and a robust version of the classic Erdos-Stone Simonovits theorem.
Subject
(authority = RUETD)
Topic
Mathematics
Subject
(authority = ETD-LCSH)
Topic
Combinatorial analysis
Subject
(authority = ETD-LCSH)
Topic
Stability
Subject
(authority = ETD-LCSH)
Topic
Graph theory
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Title
Rutgers University Electronic Theses and Dissertations
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ETD_6202
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electronic resource
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application/pdf
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text/xml
Extent
1 online resource (vi, 73 p. : ill.)
Note
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Ph.D.
Note
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Includes bibliographical references
Note
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by Simao Herdade
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TitleInfo
Title
Graduate School - New Brunswick Electronic Theses and Dissertations
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rucore19991600001
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NjNbRU
Identifier
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doi:10.7282/T30R9R7B
Genre
(authority = ExL-Esploro)
ETD doctoral
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Rights
RightsDeclaration
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The author owns the copyright to this work.
RightsHolder
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Name
FamilyName
Herdade
GivenName
Simao
Role
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Permission or license
DateTime
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2015-03-05 11:11:44
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Name
Simao Herdade
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Affiliation
Rutgers University. Graduate School - New Brunswick
AssociatedObject
Type
License
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Author Agreement License
Detail
I hereby grant to the Rutgers University Libraries and to my school the non-exclusive right to archive, reproduce and distribute my thesis or dissertation, in whole or in part, and/or my abstract, in whole or in part, in and from an electronic format, subject to the release date subsequently stipulated in this submittal form and approved by my school. I represent and stipulate that the thesis or dissertation and its abstract are my original work, that they do not infringe or violate any rights of others, and that I make these grants as the sole owner of the rights to my thesis or dissertation and its abstract. I represent that I have obtained written permissions, when necessary, from the owner(s) of each third party copyrighted matter to be included in my thesis or dissertation and will supply copies of such upon request by my school. I acknowledge that RU ETD and my school will not distribute my thesis or dissertation or its abstract if, in their reasonable judgment, they believe all such rights have not been secured. I acknowledge that I retain ownership rights to the copyright of my work. I also retain the right to use all or part of this thesis or dissertation in future works, such as articles or books.
Copyright
Status
Copyright protected
Availability
Status
Open
Reason
Permission or license
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Technical
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windows xp
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