Staff View
Some problems in extremal graph theory avoiding the use of the regularity lemma

Descriptive

TypeOfResource
Text
TitleInfo (ID = T-1)
Title
Some problems in extremal graph theory avoiding the use of the regularity lemma
Identifier
ETD_1755
Identifier (type = hdl)
http://hdl.rutgers.edu/1782.2/rucore10001600001.ETD.000051368
Language
LanguageTerm (authority = ISO639-2)
eng
Genre (authority = marcgt)
theses
Subject (ID = SBJ-1); (authority = RUETD)
Topic
Mathematics
Subject (ID = SBJ-1); (authority = ETD-LCSH)
Topic
Extremal problems (Mathematics)
Subject (ID = SBJ-1); (authority = ETD-LCSH)
Topic
Graph theory
Abstract
In this thesis we present two results in Extremal Graph Theory. The first result is a new proof of a conjecture of Bollobas on embedding trees of bounded degree. The second result is a new proof of the Posa conjecture.
Let G=(W,E) be a graph on n vertices having minimum degree at least n/2 + c log(n), where c is a constant. Bela Bollobas conjectured that every tree on n vertices with bounded degree can be embedded into G. We show that this conjecture is true. In fact we show more, that unless G is very close to either the union of two complete graphs on n/2 vertices, or the complement, then a minimum degree of n/2 is sufficient to embed any tree of bounded degree.
The k-th power of C is the graph obtained from C by joining every pair of vertices at a distance at most k in C. In 1962 Posa conjectured that any graph G of order n and minimum degree at least 2n/3 contains the square of a Hamiltonian cycle. The conjecture was proven for n > n_0 by Komlos, Sarkozy and Szemeredi using the Regularity Lemma and Blow-up Lemma. The new proof removes the use of the Regularity Lemma and establishes the Posa conjecture using combinatorial arguments, thus vastly reducing n_0.
PhysicalDescription
Form (authority = gmd)
electronic resource
Extent
vi, 59 p.
InternetMediaType
application/pdf
InternetMediaType
text/xml
Note (type = degree)
Ph.D.
Note (type = bibliography)
Includes bibliographical references (p. 57-58)
Note (type = statement of responsibility)
by Ian Marc Levitt
Name (ID = NAME-1); (type = personal)
NamePart (type = family)
Levitt
NamePart (type = given)
Ian Marc
NamePart (type = date)
1976
Role
RoleTerm (authority = RULIB); (type = )
author
DisplayForm
Ian Marc Levitt
Name (ID = NAME-2); (type = personal)
NamePart (type = family)
Szemeredi
NamePart (type = given)
Endre
Role
RoleTerm (authority = RULIB); (type = )
chair
Affiliation
Advisory Committee
DisplayForm
Endre Szemeredi
Name (ID = NAME-3); (type = personal)
NamePart (type = family)
Komlos
NamePart (type = given)
Janos
Role
RoleTerm (authority = RULIB); (type = )
internal member
Affiliation
Advisory Committee
DisplayForm
Janos Komlos
Name (ID = NAME-4); (type = personal)
NamePart (type = family)
Saks
NamePart (type = given)
Michael
Role
RoleTerm (authority = RULIB); (type = )
internal member
Affiliation
Advisory Committee
DisplayForm
Michael Saks
Name (ID = NAME-5); (type = personal)
NamePart (type = family)
Magyar
NamePart (type = given)
Akos
Role
RoleTerm (authority = RULIB); (type = )
outside member
Affiliation
Advisory Committee
DisplayForm
Akos Magyar
Name (ID = NAME-1); (type = corporate)
NamePart
Rutgers University
Role
RoleTerm (authority = RULIB); (type = )
degree grantor
Name (ID = NAME-2); (type = corporate)
NamePart
Graduate School - New Brunswick
Role
RoleTerm (authority = RULIB); (type = )
school
OriginInfo
DateCreated (point = ); (qualifier = exact)
2009
DateOther (qualifier = exact); (type = degree)
2009-05
Place
PlaceTerm (type = code)
xx
RelatedItem (type = host)
TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
Identifier (type = RULIB)
ETD
RelatedItem (type = host)
TitleInfo
Title
Graduate School - New Brunswick Electronic Theses and Dissertations
Identifier (type = local)
rucore19991600001
Location
PhysicalLocation (authority = marcorg); (displayLabel = Rutgers, The State University of New Jersey)
NjNbRU
Identifier (type = doi)
doi:10.7282/T3MC9071
Genre (authority = ExL-Esploro)
ETD doctoral
Back to the top

Rights

RightsDeclaration (AUTHORITY = GS); (ID = rulibRdec0006)
The author owns the copyright to this work.
Copyright
Status
Copyright protected
Availability
Status
Open
RightsEvent (AUTHORITY = rulib); (ID = 1)
Type
Permission or license
Detail
Non-exclusive ETD license
AssociatedObject (AUTHORITY = rulib); (ID = 1)
Type
License
Name
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.
Back to the top

Technical

ContentModel
ETD
MimeType (TYPE = file)
application/pdf
MimeType (TYPE = container)
application/x-tar
FileSize (UNIT = bytes)
348160
Checksum (METHOD = SHA1)
7381433856e6074fba1056f8550eac23e28f070d
Back to the top
Version 8.3.13
Rutgers University Libraries - Copyright ©2021