FWIW, Babai (the author) has a very small Erdos number: 1:
Let's quit beating around the bush: he has the smallest possible Erdős number[1]. If you don't presently have an Erdős number, or wish to improve your Erdős number for bragging rights, co-authoring a paper with him (or any anyone with an equivalent Erdős number) is the best possible outcome. (Obtaining an Erdős number of one is sadly no longer possible.)
> Paul Erdős has an Erdős number of zero.