Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

The group of the countable universal graph

J. K. Trussa1

a1 Department of Mathematics, Paisley College of Technology, Paisley PA 1 2BE

Let C be a set with at least two, and at most xs21350, 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 (xs2200yεdom α) Fc {x, y} = α(y).

(Received April 13 1984)