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Games, graphs, and geometry
Descriptive
TypeOfResource
Text
TitleInfo
(ID = T-1)
Title
Games, graphs, and geometry
Identifier
ETD_2634
Identifier
(type = hdl)
http://hdl.rutgers.edu/1782.1/rucore10001600001.ETD.000053616
Language
LanguageTerm
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(type = code)
eng
Genre
(authority = marcgt)
theses
Subject
(ID = SBJ-1);
(authority = RUETD)
Topic
Mathematics
Subject
(ID = SBJ-2);
(authority = ETD-LCSH)
Topic
Combinatorial geometry
Subject
(ID = SBJ-3);
(authority = ETD-LCSH)
Topic
Games
Subject
(ID = SBJ-4);
(authority = ETD-LCSH)
Topic
Charts, diagrams, etc
Subject
(ID = SBJ-5);
(authority = ETD-LCSH)
Topic
Graph theory
Abstract
(type = abstract)
This thesis concerns four separate topics: the balanced counterpart of the Hales-Jewett number, the maximal density of k-critical triangle-free graphs, Euclidean sets resilient to an 'erosion' operation, and an extension of the Local Lemma which can be applied in a game setting. For the Hales-Jewett number, our motivation comes from a desire to show that there are infinitely many 'delicate' Tic-Tac-Toe games. Roughly speaking, these are games where neither player has a simple reason for having a winning/drawing strategy. The first part of this thesis concerns the translation of bounds on the famous 'Hales-Jewett number' into bounds on the 'Halving Hales-Jewett number', its 'balanced' version, which give the desired game-theoretic consequences. The second part of this thesis concerns k-critical triangle-free graphs: can they have quadratic edge-density, independent of k as k grows large? This question has close connections both to the study of the density of critical graphs, and the study of the chromatic number of triangle-free graphs. Surprisingly, we are able to determine the exact asymptotic density of k-critical triangle-free graphs for k ≥ 6, and even for pentagon-and-triangle-free graphs. In the third part, we will consider a simple erosion operation on sets in Euclidean space, which roughly represents the operation of 'shaving off' points near the boundary of a set. We will give a complete characterization of sets whose shape is unchanged by this operation. Finally, in the fourth part, we will generalize the classical Lovasz Local Lemma to a 'Lefthanded' version, which, roughly speaking, allows one to ignore dependencies 'to the right' when making an application of the Local Lemma to bad events which have an underlying order. This will allow us to prove game-theoretic analogs of classical results on nonrepetitive sequences, representing the first successful applications of a Local Lemma to games.
PhysicalDescription
Form
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electronic resource
Extent
vi, 101 p. : ill.
InternetMediaType
application/pdf
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text/xml
Note
(type = degree)
Ph.D.
Note
Includes abstract
Note
Vita
Note
(type = bibliography)
Includes bibliographical references
Note
(type = statement of responsibility)
by Wesley Pegden
Name
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(type = personal)
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Pegden
NamePart
(type = given)
Wesley
NamePart
(type = date)
1982-
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author
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Wesley Pegden
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NamePart
(type = family)
Beck
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József
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chair
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Advisory Committee
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József Beck
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(type = personal)
NamePart
(type = family)
Kahn
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(type = given)
Jeff
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internal member
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Advisory Committee
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Jeff Kahn
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(ID = NAME-4);
(type = personal)
NamePart
(type = family)
Zeilberger
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(type = given)
Doron
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internal member
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Advisory Committee
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Doron Zeilberger
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(type = family)
Spencer
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(type = given)
Joel
Role
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outside member
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Advisory Committee
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Joel Spencer
Name
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NamePart
Rutgers University
Role
RoleTerm
(authority = RULIB)
degree grantor
Name
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NamePart
Graduate School - New Brunswick
Role
RoleTerm
(authority = RULIB)
school
OriginInfo
DateCreated
(qualifier = exact)
2010
DateOther
(qualifier = exact);
(type = degree)
2010
Place
PlaceTerm
(type = code)
xx
RelatedItem
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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
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(displayLabel = Rutgers, The State University of New Jersey)
NjNbRU
Identifier
(type = doi)
doi:10.7282/T3XP751J
Genre
(authority = ExL-Esploro)
ETD doctoral
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Rights
RightsDeclaration
(AUTHORITY = GS);
(ID = rulibRdec0006)
The author owns the copyright to this work.
Copyright
Status
Copyright protected
Availability
Status
Open
Reason
Permission or license
RightsHolder
(ID = PRH-1);
(type = personal)
Name
FamilyName
Pegden
GivenName
Wesley
Role
Copyright Holder
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(ID = RE-1);
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Type
Permission or license
DateTime
2010-04-15 14:35:37
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Role
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Name
Wesley Pegden
Affiliation
Rutgers University. Graduate School - New Brunswick
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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.
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Technical
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ETD
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application/pdf
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application/x-tar
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1198080
Checksum
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