# The group of the countable universal graph

@article{Truss1985TheGO, title={The group of the countable universal graph}, author={John Kenneth Truss}, journal={Mathematical Proceedings of the Cambridge Philosophical Society}, year={1985}, volume={98}, pages={213 - 245} }

Let C be a set with at least two, and at most ℵ0, members, and for any set X let [X]2 denote the set of its 2-element subsets. If Γ is a countable set, and Fc is a function from [Γ]2 into C, then the structure Γc = (Γ, Fc) is called the countable universal C-coloured graph if the following condition is satisfied: Whenever α is a map from a finite subset of Γ into C there is xεΓ–dom α such that (∀yεdom α) Fc {x, y} = α(y).

## 69 Citations

### An investigation of countable B-groups

- MathematicsMathematical Proceedings of the Cambridge Philosophical Society
- 1987

A group G is defined to be a B-group if any primitive permutation group which contains G as a regular subgroup is doubly transitive. In the case where G is finite the existence of families of…

### The group of almost automorphisms of the countable universal graph

- MathematicsMathematical Proceedings of the Cambridge Philosophical Society
- 1989

The group Aut Γ of automorphisms of Rado's universal graph Γ (otherwise known as the ‘random’ graph: see [1]) and the corresponding groups Aut Γc for C a set of ‘colours’ with 2 ≤ |C| ≤ ℵ0, were…

### Automorphism groups of countable algebraically closed graphs and endomorphisms of the random graph

- MathematicsMathematical Proceedings of the Cambridge Philosophical Society
- 2016

Abstract We establish links between countable algebraically closed graphs and the endomorphisms of the countable universal graph R. As a consequence we show that, for any countable graph Γ, there are…

### SOME MAXIMAL SUBGROUPS OF INFINITE SYMMETRIC GROUPS

- Mathematics
- 1996

THIS paper concerns maximal subgroups of symmetric groups on infinite, usually countable, sets. Our main aim is to give examples of maximal subgroups which could claim to be almost stabilisers of…

### Homogeneous actions on the random graph

- MathematicsGroups, Geometry, and Dynamics
- 2020

We show that any free product of two (non-trivial) countable groups, one of them being infinite, admits a faithful and homogeneous action on the Random Graph. We also show that a large class of HNN…

### Approximation of automorphisms of the rationals and the random graph

- Mathematics
- 2010

Abstract Let G be the group of order-preserving automorphisms of the rationals ℚ, or the group of colour-preserving automorphisms of the -coloured random graph . We show that given any non-identity ƒ…

### Examples and Applications of Infinite Permutation Groups

- Mathematics
- 1996

The object of this chapter is to give a selection of examples of infinite permutation groups, and a few of the ways in which permutation groups can be used in a more general context. For example, we…

### On representing words in the automorphism group of the random graph

- Mathematics
- 2006

Abstract We discuss the solubility of equations of the form w = g, where w is a word (an element of a free group FX ) and g is an element of a given group G. A word for which this equation is soluble…

### Generating Infinite Random Graphs

- MathematicsProceedings of the Edinburgh Mathematical Society
- 2018

Abstract We define a growing model of random graphs. Given a sequence of non-negative integers {dn}n=0∞ with the property that di≤i, we construct a random graph on countably infinitely many vertices…

## References

SHOWING 1-3 OF 3 REFERENCES