Embedding Problems for Graphs and Hypergraphs

Cooley, Oliver Josef Nikolaus (2010). Embedding Problems for Graphs and Hypergraphs. University of Birmingham. Ph.D.

Preview

Cooley_10_PhD.pdf PDF Download (960kB)

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.

Type of Work:	Thesis (Doctorates > Ph.D.)
Award Type:	Doctorates > Ph.D.
Supervisor(s):	Supervisor(s) Email ORCID Kuhn, Daniela UNSPECIFIED UNSPECIFIED Osthus, Deryk UNSPECIFIED UNSPECIFIED
Licence:
College/Faculty:	Colleges (2008 onwards) > College of Engineering & Physical Sciences
School or Department:	School of Mathematics
Funders:	Engineering and Physical Sciences Research Council
Subjects:	Q Science > QA Mathematics
URI:	http://etheses.bham.ac.uk/id/eprint/766

Actions

	Request a Correction
	View Item

Downloads