Proof. Peter Stadler's Erdös number is at most $3$ since we have the following sequence of joint authorships:
Babai, László, Erdös, Paul,
Selkow, Stanley M.
Random graph isomorphism. SIAM J. Comput. 9, 628-635 (1980).
Babai, László and Imrich Wilfried
On groups of polyhedral graphs. Discrete Math. 5, 101-103 (1973).
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.