Classification of Countable Homogeneous 2-Graphs

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.

Name dc:type.qualificationname

Ph.D

Level dc:type.qualificationlevel

doctoral

Grantor dc:publisher.institution

University of Leeds

Year dc:date.issued

2011

Author dc:creator

• Rose, Simon Edward

Advisor dc:contributor.advisor

• Truss, J.

Identifier

uk.bl.ethos.539681

OAI identifier oai:identifier

oai:etheses.whiterose.ac.uk:1750