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Obstacles, slopes and tic-tac-toe
Descriptive
TitleInfo
Title
Obstacles, slopes and tic-tac-toe
SubTitle
an excursion in discrete geometry and combinatorial game theory
Name
(type = personal)
NamePart
(type = family)
Mukkamala
NamePart
(type = given)
V S Padmini
NamePart
(type = date)
1983-
DisplayForm
V S Padmini Mukkamala
Role
RoleTerm
(authority = RULIB)
author
Name
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(type = family)
Szegedy
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Mario
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Mario Szegedy
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Advisory Committee
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chair
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Pach
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Janos
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Janos Pach
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Advisory Committee
Role
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co-chair
Name
(type = personal)
NamePart
(type = family)
Beck
NamePart
(type = given)
Jozsef
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Jozsef Beck
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Advisory Committee
Role
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(authority = RULIB)
internal member
Name
(type = personal)
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(type = family)
Steiger
NamePart
(type = given)
William
DisplayForm
William Steiger
Affiliation
Advisory Committee
Role
RoleTerm
(authority = RULIB)
internal member
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
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(authority = RULIB)
school
TypeOfResource
Text
Genre
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theses
OriginInfo
DateCreated
(qualifier = exact)
2011
DateOther
(qualifier = exact);
(type = degree)
2011-10
Place
PlaceTerm
(type = code)
xx
Language
LanguageTerm
(authority = ISO639-2b);
(type = code)
eng
Abstract
(type = abstract)
The minimum number of slopes used in a straight-line drawing of G is called the slope number of G. We show that every cubic graph can be drawn in the plane with straight line edges using only the four basic slopes {0, π/4, π/2,−π/4}. We also prove that four slopes have this property if and only if we can draw K4 with them. Given a graph G, an obstacle representation of G is a set of points in the plane representing the vertices of G, together with a set of obstacles (connected polygons)
such that two vertices of G are joined by an edge if and only if the corresponding points can be connected by a segment which avoids all obstacles. The obstacle number of G is the minimum number of obstacles in an obstacle representation of G. We show that there are graphs on n vertices with obstacle number (n/log n). We show that there is an m = 2n + o(n), such that, in the Maker-Breaker game played on Zd where Maker needs to put at least m of his marks consecutively in one
of n given winning directions, Breaker can force a draw using a pairing strategy. This improves the result of Kruczek and Sundberg who showed that such a pairing strategy exits if m ≥ 3n. A simple argument shows that m has to be at least 2n+1 if Breaker is only allowed to use a pairing strategy, thus the main term of our bound is optimal.
such that two vertices of G are joined by an edge if and only if the corresponding points can be connected by a segment which avoids all obstacles. The obstacle number of G is the minimum number of obstacles in an obstacle representation of G. We show that there are graphs on n vertices with obstacle number (n/log n). We show that there is an m = 2n + o(n), such that, in the Maker-Breaker game played on Zd where Maker needs to put at least m of his marks consecutively in one
of n given winning directions, Breaker can force a draw using a pairing strategy. This improves the result of Kruczek and Sundberg who showed that such a pairing strategy exits if m ≥ 3n. A simple argument shows that m has to be at least 2n+1 if Breaker is only allowed to use a pairing strategy, thus the main term of our bound is optimal.
Subject
(authority = RUETD)
Topic
Mathematics
Subject
(authority = ETD-LCSH)
Topic
Combinatorial analysis
Subject
(authority = ETD-LCSH)
Topic
Discrete geometry
Subject
(authority = ETD-LCSH)
Topic
Mathematical models
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
Identifier
ETD_3564
Identifier
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http://hdl.rutgers.edu/1782.1/rucore10001600001.ETD.000063727
PhysicalDescription
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electronic resource
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application/pdf
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text/xml
Extent
vii, 71 p. : ill.
Note
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Ph.D.
Note
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Includes bibliographical references
Note
(type = vita)
Includes vita
Note
(type = statement of responsibility)
by V S Padmini Mukkamala
Location
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NjNbRU
Identifier
(type = doi)
doi:10.7282/T3XD10QD
Genre
(authority = ExL-Esploro)
ETD doctoral
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Rights
RightsDeclaration
(ID = rulibRdec0006)
The author owns the copyright to this work.
RightsHolder
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Name
FamilyName
Mukkamala
GivenName
V S Padmini
Role
Copyright Holder
RightsEvent
Type
Permission or license
DateTime
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(qualifier = exact);
(point = start)
2011-09-15 13:55:12
AssociatedEntity
Name
V S Padmini Mukkamala
Role
Copyright holder
Affiliation
Rutgers University. Graduate School - New Brunswick
AssociatedObject
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.
Copyright
Status
Copyright protected
Availability
Status
Open
Reason
Permission or license
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