Topics in finite graph Ramsey theory

Simple item page
dc.contributor.authorBorgersen, Robert David
dc.contributor.examiningcommitteeDoob, Michael (Mathematics) Kocay, William (Computer Science) Platt, Craig (Mathematics)en
dc.contributor.supervisorGunderson, David (Mathematics)en
dc.date.accessioned2008-01-18T15:05:39Z
dc.date.available2008-01-18T15:05:39Z
dc.date.issued2008-01-18T15:05:39Z
dc.degree.disciplineMathematicsen_US
dc.degree.levelMaster of Science (M.Sc.)en_US
dc.description.abstractFor 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.description.noteFebruary 2008en
dc.format.extent1544379 bytes
dc.format.mimetypeapplication/pdf
dc.identifier.urihttp://hdl.handle.net/1993/2998
dc.language.isoengen_US
dc.rightsopen accessen_US
dc.subjectRamseyen
dc.subjectgraphen
dc.subjectRamsey theoryen
dc.subjectgraph theoryen
dc.subjectRamsey's theoremen
dc.subjectRamsey numbersen
dc.subjectgraph Ramseyen
dc.subjectinduced graph Ramseyen
dc.subjectextremal graphen
dc.subjectRamsey graphen
dc.subjectlinear Ramseyen
dc.subjectrestricted Ramseyen
dc.subjectRamsey minimalen
dc.subjectminimal Ramseyen
dc.subjectRamsey arrowen
dc.titleTopics in finite graph Ramsey theoryen
dc.typemaster thesisen_US
Files
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
Borgersen-2007-Topics in finite graph Ramsey theory-Thesis.pdf
Size:
1.47 MB
Format:
Adobe Portable Document Format
Description:
Download
License bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
license.txt
Size:
2.35 KB
Format:
Item-specific license agreed to upon submission
Description:
Download
Collections
FGS - Electronic Theses and Practica