Some rigid moieties of homogeneous graphs

Any countable Kn-free graph T embeds as a moiety into the universal homogeneous Kn-free graph Kn in such a way that every automorphism of T extends into a unique automorphism of Kn. Furthermore, there are 2ω such embeddings which are pairwise not conjugate under Aut(Kn)

Some rigid moieties of homogeneous graphs

Any countable Kn-free graph T embeds as a moiety into the universal homogeneous Kn-free graph Kn in such a way that every automorphism of T extends into a unique automorphism of Kn. Furthermore, there are 2ω such embeddings which are pairwise not conjugate under Aut(Kn)

Multicoloured Random Graphs: Constructions and Symmetry

This is a research monograph on constructions of and group actions on countable homogeneous graphs, concentrating particularly on the simple random graph and its edge-coloured variants. We study various aspects of the graphs, but the emphasis is on understanding those groups that are supported by these graphs together with links with other structures such as lattices, topologies and filters, rings and algebras, metric spaces, sets and models, Moufang loops and monoids. The large amount of background material included serves as an introduction to the theories that are used to produce the new results. The large number of references should help in making this a resource for anyone interested in beginning research in this or allied fields.Comment: Index added in v2. This is the first of 3 documents; the other 2 will appear in physic