Embedding Problems for Graphs and Hypergraphs

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http://eprints.org/relation/isVolatileVersionOf http://etheses.bham.ac.uk/id/document/1860 http://eprints.org/relation/ispreviewThumbnailVersionOf http://etheses.bham.ac.uk/id/document/1860 http://eprints.org/relation/isVersionOf http://etheses.bham.ac.uk/id/document/1860 archive 4031 disk0/00/00/07/66 2010-09-20 11:16:46 2019-01-23 09:52:48 2011-07-19 16:22:59 thesis show 0 Cooley Oliver Josef Nikolaus Kuhn Daniela Osthus Deryk University of Birmingham Embedding Problems for Graphs and Hypergraphs unpub QA 10col_ephy 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applications to Ramsey numbers which improve upon previously known results. 2010-07 2009-10 graduation eng This unpublished thesis/dissertation is copyright of the author and/or third parties. The intellectual property rights of the author or third parties in respect of this work are as defined by The Copyright Designs and Patents Act 1988 or as modified by any successor legislation. Any use made of information contained in this thesis/dissertation must be in accordance with that legislation and must be properly acknowledged. Further distribution or reproduction in any format is prohibited without the permission of the copyright holder. public University of Birmingham School of Mathematics d_ph epsrc 2010-07 graduation