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dc.contributor.supervisor Gunderson, David (Mathematics) en
dc.contributor.author Borgersen, Robert David
dc.date.accessioned 2008-01-18T15:05:39Z
dc.date.available 2008-01-18T15:05:39Z
dc.date.issued 2008-01-18T15:05:39Z
dc.identifier.uri http://hdl.handle.net/1993/2998
dc.description.abstract For a positive integer $r$ and graphs $F$, $G$, and $H$, the graph Ramsey arrow notation $F \longrightarrow (G)^H_r$ means that for every $r$-colouring of the subgraphs of $F$ isomorphic to $H$, there exists a subgraph $G'$ of $F$ isomorphic to $G$ such that all the subgraphs of $G'$ isomorphic to $H$ are coloured the same. Graph Ramsey theory is the study of the graph Ramsey arrow and related arrow notations for other kinds of ``graphs" (\emph{e.g.}, ordered graphs, or hypergraphs). This thesis surveys finite graph Ramsey theory, that is, when all structures are finite. One aspect surveyed here is determining for which $G$, $H$, and $r$, there exists an $F$ such that $F \longrightarrow (G)^H_r$. The existence of such an $F$ is guaranteed when $H$ is complete, whether ``subgraph" means weak or induced, and existence results are also surveyed when $H$ is non-complete. When such an $F$ exists, other aspects are surveyed, such as determining the order of the smallest such $F$, finding such an $F$ in some restricted family of graphs, and describing the set of minimal such $F$'s. en
dc.format.extent 1544379 bytes
dc.format.mimetype application/pdf
dc.language.iso en_US
dc.rights info:eu-repo/semantics/openAccess
dc.subject Ramsey en
dc.subject graph en
dc.subject Ramsey theory en
dc.subject graph theory en
dc.subject Ramsey's theorem en
dc.subject Ramsey numbers en
dc.subject graph Ramsey en
dc.subject induced graph Ramsey en
dc.subject extremal graph en
dc.subject Ramsey graph en
dc.subject linear Ramsey en
dc.subject restricted Ramsey en
dc.subject Ramsey minimal en
dc.subject minimal Ramsey en
dc.subject Ramsey arrow en
dc.title Topics in finite graph Ramsey theory en
dc.type info:eu-repo/semantics/masterThesis
dc.degree.discipline Mathematics en
dc.contributor.examiningcommittee Doob, Michael (Mathematics) Kocay, William (Computer Science) Platt, Craig (Mathematics) en
dc.degree.level Master of Science (M.Sc.) en
dc.description.note February 2008 en


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