** Proof.**
Peter Stadler's Erdös number is at most $3$ since
we have the following sequence of joint authorships:

0454.05038
**Babai, László**, *Erdös, Paul*,
Selkow, Stanley M.

Random graph isomorphism.
SIAM J. Comput. 9, 628-635 (1980).

0261.05116
*Babai, László* and **Imrich Wilfried**

On groups of polyhedral graphs.
Discrete Math. 5, 101-103 (1973).

pre01833092
*Imrich, Wilfried* and **Stadler, Peter F.**

Minimum Cycle Bases of Product Graphs

Australasian J. Comb. 26: 233-244 (2002).

On the other hand, Peter Stadler has not written a joint paper with anyone listed in the file of Paul Erdös' coauthors, thus my Erdös number is strictly larger than 2.

**q.e.d.**