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Spanning subgraphs in graphs and hypergraphs
Descriptive
TitleInfo
Title
Spanning subgraphs in graphs and hypergraphs
Name
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(type = family)
Khan
NamePart
(type = given)
Imdadullah
NamePart
(type = date)
1980-
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Imdadullah Khan
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author
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Szemeredi
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Endre
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Endre Szemeredi
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Advisory Committee
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chair
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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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Grigoriadis
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Michael
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Michael Grigoriadis
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Advisory Committee
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internal member
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Reed
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Bruce
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Bruce Reed
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Advisory Committee
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Rutgers University
Role
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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
DateCreated
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2011
DateOther
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(type = degree)
2011-05
Place
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(type = code)
xx
Language
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(type = code)
eng
Abstract
(type = abstract)
This thesis consists of three new fundamental results on the existence of spanning subgraphs in graphs and hypergraphs. Cycle Factors in Graphs: A classical conjecture of El-Zahar states that if H is a graph consisting of r vertex disjoint cycles of length n_1, n_2, ldots , n_r, and G is a graph on n = n_1+n_2 + ... +n_r vertices with minimum degree at least [sigmar/i=1 n_1/2
then G contains H as a subgraph. A proof of this conjecture for graphs withn[greater than or less than] n_0 was announced by S. Abbasi (1998) using the Regularity Lemma-Blow-up Lemma method. We give a new, ``de-regularized" proof of the conjecture for large graphs that avoids the use of the Regularity Lemma, and thus the resulting n_0 is much smaller. Perfect Matching in three-uniform hypergraphs A perfect matching in a three-uniform hypergraph on n=3k vertices is a subset of n/3 disjoint edges. We prove that if $H$ is a three-uniform hypergraph on $n=3k$ vertices such that every vertex belongs to at least {n-1choose 2} - {2n/3choose 2}+1 edges, then H contains a perfect matching. We give a construction to show that our result is best possible. Perfect Matching in four-uniform hypergraphs A perfect matching in a four-uniform hypergraph is a subset of lfloorfrac{n}{4}
floor disjoint edges. We prove that if H is a sufficiently large four-uniform hypergraph on n=4k vertices such that every vertex belongs to more than ${n-1choose 3} - {3n/4 choose 3} edges, then H contains a perfect matching. Our bound is tight and settles a conjecture of Hán, Person and Schacht (2009).
then G contains H as a subgraph. A proof of this conjecture for graphs withn[greater than or less than] n_0 was announced by S. Abbasi (1998) using the Regularity Lemma-Blow-up Lemma method. We give a new, ``de-regularized" proof of the conjecture for large graphs that avoids the use of the Regularity Lemma, and thus the resulting n_0 is much smaller. Perfect Matching in three-uniform hypergraphs A perfect matching in a three-uniform hypergraph on n=3k vertices is a subset of n/3 disjoint edges. We prove that if $H$ is a three-uniform hypergraph on $n=3k$ vertices such that every vertex belongs to at least {n-1choose 2} - {2n/3choose 2}+1 edges, then H contains a perfect matching. We give a construction to show that our result is best possible. Perfect Matching in four-uniform hypergraphs A perfect matching in a four-uniform hypergraph is a subset of lfloorfrac{n}{4}
floor disjoint edges. We prove that if H is a sufficiently large four-uniform hypergraph on n=4k vertices such that every vertex belongs to more than ${n-1choose 3} - {3n/4 choose 3} edges, then H contains a perfect matching. Our bound is tight and settles a conjecture of Hán, Person and Schacht (2009).
Subject
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Topic
Computer Science
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Title
Rutgers University Electronic Theses and Dissertations
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ETD_3293
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electronic resource
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Extent
x, 105 p. : ill.
Note
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Ph.D.
Note
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Includes bibliographical references
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Includes vita
Note
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by Imdadullah Khan
Subject
(authority = ETD-LCSH)
Topic
Graph theory
Subject
(authority = ETD-LCSH)
Topic
Hypergraphs
Identifier
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http://hdl.rutgers.edu/1782.1/rucore10001600001.ETD.000061299
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Graduate School - New Brunswick Electronic Theses and Dissertations
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rucore19991600001
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Identifier
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doi:10.7282/T3C24VSC
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(authority = ExL-Esploro)
ETD doctoral
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Rights
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The author owns the copyright to this work.
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Name
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Khan
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Imdadullah
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Permission or license
DateTime
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2011-04-14 12:27:55
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Imdadullah Khan
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Affiliation
Rutgers University. Graduate School - New Brunswick
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Author Agreement License
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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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2011-05-31
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2011-11-30
Type
Embargo
Detail
Access to this PDF has been restricted at the author's request. It will be publicly available after November 30th, 2011.
Copyright
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Copyright protected
Availability
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Open
Reason
Permission or license
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