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.
| Identifer | oai:union.ndltd.org:uvic.ca/oai:dspace.library.uvic.ca:1828/2909 |
| Date | 23 July 2010 |
| Creators | Chan, Justin |
| Contributors | Dukes, Peter |
| Source Sets | University of Victoria |
| Language | English, English |
| Detected Language | English |
| Type | Thesis |
| Rights | Available to the World Wide Web |
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