Erdös Lap Number

Definition:

Erdös is the only person with the Erdös Lap Number 0.
In order to acquire the Erdös Lap Number i one has to sit on a lap of a person with the number i-1.

NB: A proof (in a form of a photo or a notary certification) is required for any claims.

For example, Barbie Freidin (née Benzer) has the Erdös Lap Number of 1. On this photo (taken from the Fall 1996 issue of "Math PUrview") she is the leftmost epsilon.
Therefore, Oleg Pikhurko gets the the Erdös Lap Number 2. On the photo he is the O(1) (the O big of one) sitting on Barbie's lap.

Note: The Erdös Lap Number of 3 is not for sale or exchange but polite requests from persons weighting not more than 300lb will be considered. -OP

Open Question (Małgorzata Bednarska $10): Does there exist a person whose

(usual) Erdös Number = Erdös Lap Number = 1 ?

Peter Griztmann conjectured that the answer is "Yes" and that János Pach is such a person. Unfortunately, even János himself was not able to produce a proof that his Erdös Lap Number is 1 (although he said that "it is a reasonable conjecture").

The following photo (posted by János Pach on Gil Kalai's blog) led some people to believe that they have a promising approach to the proof. However, Uncle Paul holds not János but his daughter...

Erdos and Pach

The Erdös Lap Graph is expanding!...

Erdos lap number 3 comes as an extra bonus for 21-484 "Graph Theory" students:

Sometimes I'm recognized even in public transport :-)
Anders