# Multicoloured Random Graphs: Constructions and Symmetry

@inproceedings{Tarzi2015MulticolouredRG, title={Multicoloured Random Graphs: Constructions and Symmetry}, author={Sam Tarzi}, year={2015} }

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…

## Figures from this paper

## 4 Citations

Near actions.

- Mathematics
- 2019

A near permutation of a set is a bijection between two cofinite subsets, modulo coincidence on smaller cofinite subsets. Near permutations of a set form its near symmetric group. In this monograph,…

A topological characterisation of endomorphism monoids of countable structures

- Mathematics
- 2015

A topological monoid is isomorphic to an endomorphism monoid of a countable structure if and only if it is separable and has a compatible complete ultrametric such that composition from the left is…

Topology is relevant (in a dichotomy conjecture for infinite-domain constraint satisfaction problems)

- Mathematics, Computer Science2019 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)
- 2019

It is shown that local satisfaction and global satisfaction of nontrivial height 1 identities differ for $\omega$ -categorical structures with less than double exponential orbit growth, thereby resolving one of the main open problems in the algebraic theory of such structures.

The algebraic dichotomy conjecture for infinite domain Constraint Satisfaction Problems

- Computer Science, Mathematics2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)
- 2016

We prove that an ω-categorical core structure primitively positively interprets all finite structures with parameters if and only if some stabilizer of its polymorphism clone has a homomorphism to…

## References

SHOWING 1-10 OF 528 REFERENCES

Oligomorphic groups and homogeneous graphs

- Mathematics
- 1997

These notes are, in a sense, an elaboration on the comments on pages 232-234 of the book [10] on Distance-regular Graphs by Brouwer, Cohen and Neumaier. Apart from these brief comments, the book is…

Infinite Locally Random Graphs

- Computer Science, MathematicsInternet Math.
- 2007

It is shown that there are in fact infinitely many isomorphism classes of limit graph, and a classification is given and the inexhaustibility of these graphs is considered.

Designs, graphs, codes, and their links

- Computer Science
- 1991

The authors have considerably reworked and expanded their earlier successful books on designs, graphs and codes, into an invaluable textbook that is accessible to any student with a background of undergraduate algebra.

Automorphisms of graphs

- Mathematics
- 2003

This chapter surveys automorphisms of finite graphs, concentrating on the asymmetry of typical graphs, prescribing automorphism groups (as either permutation groups or abstract groups), and special…

Cofinitary Permutation Groups

- Mathematics
- 1996

A permutation group is cofinitary if any non-identity element fixes only finitely many points. This paper presents a survey of such groups. The paper has four parts. Sections 1-6 develop some basic…

Partitions and orientations of the Rado graph

- Mathematics
- 2006

We classify the countably infinite oriented graphs which, for every partition of their vertex set into two parts, induce an isomorphic copy of themselves on at least one of the parts. These graphs…

Edge partitions of the Rado graph

- Mathematics, Computer ScienceComb.
- 1996

It is proved that for every colouring of the edges of the Rado graph,ℛ, with finitely many coulours, it contains an isomorphic copy whose edges are coloured with at most two of the colours.

Finite presentation of homogeneous graphs, posets and Ramsey classes

- Mathematics
- 2005

It is commonly believed that one can prove Ramsey properties only for simple and “well behaved” structures. This is supported by the link of Ramsey classes of structures with homogeneous structures.…

On the action of a group on a graph

- Mathematics
- 1992

The present paper was written at the request of one of the editors for a survey on some results of the author. The research presents an approach to studying groups acting on connected…

Uncountable graphs and invariant measures on the set of universal countable graphs

- Mathematics
- 2010

We give new examples and describe the complete lists of all measures on the set of countable homogeneous universal graphs and Ks-free homogeneous universal graphs (for s ≥ 3) that are invariant with…