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

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Abstract
We classify certain families of homogeneous 2graphs and prove some results that apply to families of 2graphs that we have not completely classified. We classify homogeneous 2coloured 2graphs where one component is a disjoint union of complete graphs and the other is the random graph or the generic Krfree graph for some r. We show that any nontrivial examples are derived from a homogeneous 2coloured 2graph where one component is the complete graph and the other is the random graph or the generic Krfree graph for some r; and these are in turn either generic or equivalent to one that minimally omits precisely one monochromatic colour1 (K1,Kt) 2graph for some t < r. We also classify homogeneous 2coloured 2graphs G where both components are isomorphic and each is either the random graph or the generic K3free graph; in both cases show that there is an antichain A of monochromatic colour1 2graphs all of the form (Ks,Kt) (for some s and t) such that G is equivalent to the homogeneous 2coloured 2graph 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 