Asymptotic existence results on specific graph decompositions
Date
2010-07-23T19:45:11Z
Authors
Chan, Justin
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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.
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Keywords
combinatorics, combinatorial, design, graph, frame, frames, designs, resolvable, group, divisible