Perfect T(G) triple systems when G is a matching
| dc.contributor.author | Manzer, Joshua Daniel Adrian | |
| dc.date.issued | 2008 | |
| dc.description.abstract | A T(G) triple is formed by taking a graph G and replacing every edge with a 3-cycle, where all of the new vertices are distinct from all others in G. An edge-disjoint decomposition of 3Kn into T(G) triples is called a T(G) triple system of order n. If we can decompose Kn into copies of a graph G, such that we can form a T(G) triple from each graph in the decomposition and produce a partition of the edges of 3Kn, then the resulting T(G) triple system is called perfect. -- We give necessary and sufficient conditions for the existence of perfect T(G) triple systems when G is a matching with λ edges, which we denote by ⋃λP₂. We then give cyclic perfect decompositions of 3Kn into T(⋃λP₂) triples for all n ≡ 1 (mod 2λ) when λ is even (except for n = 4λ + 1 when λ > 8) as well as completely solve the case λ = 3. | |
| dc.description.note | Includes bibliographical references (leaves [100]-102). | |
| dc.format.extent | xi, 102 leaves : ill. | |
| dc.format.medium | Text | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14783/1859 | |
| dc.language.iso | en | |
| dc.publisher | Memorial University of Newfoundland | |
| dc.rights.license | The author retains copyright ownership and moral rights in this thesis. Neither the thesis nor substantial extracts from it may be printed or otherwise reproduced without the author's permission. | |
| dc.subject.lcsh | Decomposition (Mathematics) | |
| dc.subject.lcsh | Graph theory | |
| dc.subject.lcsh | Incomplete block designs | |
| dc.title | Perfect T(G) triple systems when G is a matching | |
| dc.type | Master thesis | |
| mem.campus | St. John's Campus | |
| mem.convocationDate | 2008 | |
| mem.department | Mathematics and Statistics | |
| mem.divisions | MathStat | |
| mem.faculty | Faculty of Science | |
| mem.fullTextStatus | public | |
| mem.institution | Memorial University of Newfoundland | |
| mem.isPublished | unpub | |
| mem.thesisAuthorizedName | Manzer, Joshua Daniel Adrian, 1984- | |
| thesis.degree.discipline | Mathematics and Statistics | |
| thesis.degree.grantor | Memorial University of Newfoundland | |
| thesis.degree.level | masters | |
| thesis.degree.name | M. Sc. |
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