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# Topics in finite graph Ramsey theory

 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. en 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. 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.type master thesis en_US dc.degree.discipline Mathematics en dc.contributor.examiningcommittee Doob, Michael (Mathematics) en Kocay, William (Computer Science) Platt, Craig (Mathematics) dc.degree.level Master of Science (M.Sc.) en dc.description.note February 2008 en
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