Asymptotic existence results on specific graph decompositions
| dc.contributor.author | Chan, Justin | |
| dc.contributor.supervisor | Dukes, Peter | |
| dc.date.accessioned | 2010-07-23T19:45:11Z | |
| dc.date.available | 2010-07-23T19:45:11Z | |
| dc.date.copyright | 2010 | en |
| dc.date.issued | 2010-07-23T19:45:11Z | |
| dc.degree.department | Department of Mathematics and Statistics | |
| dc.degree.level | Master of Science M.Sc. | en |
| dc.description.abstract | This work examines various asymptotic edge-decomposition problems on graphs. A G-group divisible design (G-GDD) of type [g_1, ..., g_u] and index lambda is a decomposition of the edges of the complete lambda-fold multipartite graph H, with groups (maximal independent sets) G_1, ..., G_n, |G_i| = g_i, into graphs (blocks) isomorphic to G. We shall also examine special types of G-GDDs (such as G-frames) and prove that, given all parameters except u, these structures exist for all asymptotically large u satisfying the necessary conditions. Our primary technique is to invoke a useful theorem of Lamken and Wilson on edge-colored graph decompositions. The basic construction for k-RGDDs shall be outlined at the end of the thesis. | en |
| dc.identifier.uri | http://hdl.handle.net/1828/2909 | |
| dc.language | English | eng |
| dc.language.iso | en | en |
| dc.rights | Available to the World Wide Web | en |
| dc.subject | combinatorics | en |
| dc.subject | combinatorial | en |
| dc.subject | design | en |
| dc.subject | graph | en |
| dc.subject | frame | en |
| dc.subject | frames | en |
| dc.subject | designs | en |
| dc.subject | resolvable | en |
| dc.subject | group | en |
| dc.subject | divisible | en |
| dc.subject.lcsh | UVic Subject Index::Sciences and Engineering::Mathematics::Pure mathematics | en |
| dc.title | Asymptotic existence results on specific graph decompositions | en |
| dc.type | Thesis | en |