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Classification of Countable Homogeneous 2-Graphs

Rose, Simon Edward (2011) Classification of Countable Homogeneous 2-Graphs. PhD thesis, University of Leeds.

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Abstract

We classify certain families of homogeneous 2-graphs and prove some results that apply to families of 2-graphs that we have not completely classified. We classify homogeneous 2-coloured 2-graphs where one component is a disjoint union of complete graphs and the other is the random graph or the generic Kr-free graph for some r. We show that any non-trivial examples are derived from a homogeneous 2-coloured 2-graph where one component is the complete graph and the other is the random graph or the generic Kr-free graph for some r; and these are in turn either generic or equivalent to one that minimally omits precisely one monochromatic colour-1 (K1,Kt) 2-graph for some t < r. We also classify homogeneous 2-coloured 2-graphs G where both components are isomorphic and each is either the random graph or the generic K3-free graph; in both cases show that there is an antichain A of monochromatic colour-1 2-graphs all of the form (Ks,Kt) (for some s and t) such that G is equivalent to the homogeneous 2-coloured 2-graph with the specified components that is generic subject to minimally omitting the elements of A.

Item Type: Thesis (PhD)
Academic Units: The University of Leeds > Faculty of Maths and Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds)
Depositing User: Ethos Import
Date Deposited: 25 Oct 2011 10:15
Last Modified: 07 Mar 2014 11:24
URI: http://etheses.whiterose.ac.uk/id/eprint/1750

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