Use this URL to cite or link to this record in EThOS: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.520331
Title: Embedding Problems for Graphs and Hypergraphs
Author: Cooley, Oliver Josef Nikolaus
Awarding Body: University of Birmingham
Current Institution: University of Birmingham
Date of Award: 2010
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Abstract:
This thesis deals with the problem of finding some substructure within a large graph or hypergraph. In the case of graphs, we consider the substructures consisting of fixed subgraphs or families of subgraphs, perfect graph 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 proofs of three new embedding results, two for graphs and one for hypergraphs. I will also discuss the regularity lemma for graphs and hypergraphs, an important tool which underpins these and many similar embedding results. Finally, I will also discuss graph and hypergraph Ramsey numbers, since two of the embedding results have important applications to Ramsey numbers which improve upon previously known results.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.520331  DOI: Not available
Keywords: QA Mathematics
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