# The random graph and its relations

## Prof. Peter J Cameron, Queen Mary, University of London

In 1963, Erdős and Rényi proved the astonishing result that, if a countably infinite graph is chosen at random by selecting edges independently, there is one particular graph which will almost surely arise: this is the celebrated “random graph”. This graph is met with in many different parts of mathematics, including logic, group theory, Ramsey theory, and topological dynamics. I will talk about it and some of its properties, and some related structures.