Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 78 for “"Hypergraphs"”.
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Universal Hypergraphs.
<p>In this thesis, we study universal hypergraphs. What are these? Let us start with defining a universal graph as a graph on <em>n</em> vertices that contains each of the many possible graphs of a smaller size <em>k</em> < <em>n</em> as an induced subgraph. A <em>hypergraph</em> is a discrete …
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Coloring clique hypergraphs
… s-coloring of CH(G). We prove that the clique hypergraphs of chordal and comparability graphs are bicolorable and that the clique hypergraphs of circular-arc graphs are 3-colorable. Our main result is the characterization of (W, 2)-extendibility for chordal graphs in the case when W=2 .
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Spectra of Hypergraphs
<p>We present a spectral theory of uniform hypergraphs that closely parallels Spectral Graph Theory. A number of developments building upon classical work has led to a rich understanding of 'symmetric hyperdeterminants' of hypermatrices, a.k.a. multidimensional arrays. Symmetric hyperdeterminants …
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Eulerian Properties of Design Hypergraphs and Hypergraphs with Small Edge Cuts
… --- treatment of this subject has only begun on hypergraphs in the last decade. Other authors have produced results about rank-2 universal cycles and 1-overlap cycles, which are equivalent to our definition of Euler tours. In contrast, an Euler family is a collection of nontrivial closed walks …
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Extremal Problems for Hypergraphs
We study various extremal problems on hypergraphs
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Matching problems in hypergraphs
… by 3, if F_1, ..., F_{n/3} are 3-uniform hypergraphs with a common vertex set and the minimum vertex degree in each F_i is greater than {(n-1) choose 2} - {2n/3 choose 2} for i = 1, ..., n/3, then the family {F_1, ..., F_{n/3}} admits a rainbow matching, i.e., a matching consisting of one …
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Learning on Inhomogeneous Hypergraphs
… relations. Such relations can be modeled by hypergraphs, where the notion of an edge is generalized to a hyperedge that can connect more than two vertices. Traditional hypergraph models treat all the vertices in a hyperedge equally while in practice these vertices might contribute differently …
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On hypergraphs and hypergeometries.
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 1971
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On optimal structures in hypergraphs
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2024-09-16 without embargo terms
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Embedding problems in graphs and hypergraphs
The first part of this thesis concerns perfect matchings and their generalisations. We determine the minimum vertex degree that ensures a perfect matching in a 3-uniform hypergraph, thereby answering a question of Hàn, Person and Schacht. We say that a graph \(G\) has a perfect \(H\)-packing (also …
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Embedding Problems for Graphs and Hypergraphs
… packings and spanning subgraphs. In the case of hypergraphs we consider the substructure consisting of a hypergraph whose order is linear in the order of the large hypergraph. I will show how these problems are extensions of more basic and well-known results in graph theory. I will give full …
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Coloring Problems on Graphs and Hypergraphs
… Similar bounds hold for a generalization to hypergraphs.
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Problems and results on linear hypergraphs
… involving the study of 3-uniform, linear hypergraphs satisfying some additional structural constraint. We begin with a problem of Hrushovski concerning Latin squares satisfying a partial associativity condition. From an $n\times n$ Latin square $A$ one can define a binary operation …
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Extremal problems on hypergraphs and set families
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-10-19 without embargo terms
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Cuts and connectivity in graphs and hypergraphs
… and connectivity problems on graphs, digraphs, hypergraphs and hedgegraphs. The main results are the following: - We introduce a faster algorithm for finding the reduced graph in element-connectivity computations. We also show its application to node separation. - We present several results on …
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The regularity method in directed graphs and hypergraphs
In recent years the regularity method has been used to tackle many embedding problems in extremal graph theory. This thesis demonstrates and develops three different techniques which can be used in conjunction with the regularity method to solve such problems. These methods enable us to prove an …
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Colorings and list colorings of graphs and hypergraphs
Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2012-04-04T13:50:38Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 3 thesis.tex: 208138 bytes, checksum: 3f2bbfe42b155982f3fe9f0f51b4e863 (MD5) config1.eps: 12369 bytes, checksum: …
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Covering and packing problems on graphs and hypergraphs
Item reinstated by Sarah Shreeves (sshreeve@illinois.edu) on 2013-08-27T10:00:22Z Item was in collections: University of Illinois Dissertations and Theses (ID: 204) Dissertations and Theses - Mathematics (ID: 749) No. of bitstreams: 3 Stocker_Christopher.pdf.txt: 236192 bytes, checksum: …
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Extremal problems for cycles in graphs and hypergraphs
… of Turan type problems in graphs and hypergraphs. In particular, we focus on graphs and hypergraphs without long cycles or long paths, extending famous results of Erdos and Gallai. Results include bounds on the size of such objects as well as stability theorems about the structure of …
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Semi-algebraic graphs and hypergraphs in incidence geometry
… have a large intersection? As most graphs and hypergraphs arising from problems in discrete geometry are semi-algebraic, our results have applications to discrete geometry. The main tools used in our proofs include some version of polynomial partitioning, a Milnor-Thom-type result from topology …
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