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Two problems on cycles in random graphs

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TitleInfo
Title
Two problems on cycles in random graphs
Name (type = personal)
NamePart (type = family)
Baron
NamePart (type = given)
Jacob D.
NamePart (type = date)
1988-
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Jacob D. Baron
Role
RoleTerm (authority = RULIB)
author
Name (type = personal)
NamePart (type = family)
Kahn
NamePart (type = given)
Jeff
DisplayForm
Jeff Kahn
Affiliation
Advisory Committee
Role
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chair
Name (type = personal)
NamePart (type = family)
Komlos
NamePart (type = given)
Janos
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Janos Komlos
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Advisory Committee
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internal member
Name (type = personal)
NamePart (type = family)
Saks
NamePart (type = given)
Michael
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Michael Saks
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Advisory Committee
Role
RoleTerm (authority = RULIB)
internal member
Name (type = personal)
NamePart (type = family)
Yuster
NamePart (type = given)
Raphael
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Raphael Yuster
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Advisory Committee
Role
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outside member
Name (type = corporate)
NamePart
Rutgers University
Role
RoleTerm (authority = RULIB)
degree grantor
Name (type = corporate)
NamePart
Graduate School - New Brunswick
Role
RoleTerm (authority = RULIB)
school
TypeOfResource
Text
Genre (authority = marcgt)
theses
OriginInfo
DateCreated (qualifier = exact)
2016
DateOther (qualifier = exact); (type = degree)
2016-10
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2016
Place
PlaceTerm (type = code)
xx
Language
LanguageTerm (authority = ISO639-2b); (type = code)
eng
Abstract (type = abstract)
We prove three results. First, an old conjecture of Zs. Tuza says that for any graph G, the ratio of the minimum size, τ3(G), of a set of edges meeting all triangles to the maximum size, ν3(G), of an edge-disjoint triangle packing is at most 2. Disproving a conjecture of R. Yuster [40], we show that for any fixed, positive α there are arbitrarily large graphs G of positive density satisfying τ3(G) > (1 − o(1))|G|/2 and ν3(G) < (1 + α)|G|/4. Second, write C(G) for the cycle space of a graph G, Cκ(G) for the subspace of C(G) spanned by the copies of Cκ in G, Tκ for the class of graphs satisfying Cκ(G) = C(G), and Qκ for the class of graphs each of whose edges lies in a Cκ. We prove that for every odd κ ≥ 3 and G = Gn,p, max p Pr(G ∈ Qκ Tκ) → 0; so the Cκ’s of a random graph span its cycle space as soon as they cover its edges. For κ = 3 this was shown in [12]. Third, we extend the seminal van den Berg–Kesten Inequality [9] on disjoint occurrence of two events to a setting with arbitrarily many events, where the quantity of interest is the maximum number that occur disjointly. This provides a handy tool for bounding upper tail probabilities for event counts in a product probability space.
Subject (authority = RUETD)
Topic
Mathematics
Subject (authority = ETD-LCSH)
Topic
Random graphs
RelatedItem (type = host)
TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
Identifier (type = RULIB)
ETD
Identifier
ETD_7578
PhysicalDescription
Form (authority = gmd)
electronic resource
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application/pdf
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text/xml
Extent
1 online resource (vi, 94 p. : ill.)
Note (type = degree)
Ph.D.
Note (type = bibliography)
Includes bibliographical references
Note (type = statement of responsibility)
by Jacob D. Baron
RelatedItem (type = host)
TitleInfo
Title
Graduate School - New Brunswick Electronic Theses and Dissertations
Identifier (type = local)
rucore19991600001
Location
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NjNbRU
Identifier (type = doi)
doi:10.7282/T39C70QR
Genre (authority = ExL-Esploro)
ETD doctoral
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RightsDeclaration (ID = rulibRdec0006)
The author owns the copyright to this work.
RightsHolder (type = personal)
Name
FamilyName
Baron
GivenName
Jacob
MiddleName
D.
Role
Copyright Holder
RightsEvent
Type
Permission or license
DateTime (encoding = w3cdtf); (qualifier = exact); (point = start)
2016-09-16 02:39:19
AssociatedEntity
Name
Jacob Baron
Role
Copyright holder
Affiliation
Rutgers University. Graduate School - New Brunswick
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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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2016-09-16T02:06:14
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