Brian Pinsky, Rutgers University

Abstract

What is the probability the following graphs are isomorphic?

1. Two random graphs random graphs on n verticies with probability p.
2. Two random graphs random graphs on  verticies with probability p.
3. Two random graphs random graphs on ^ verticies with probability p. 

Question 1 is way too hard for me; I will say nothing about it.

Question 2 is easy, and we will answer it Wednesday.  That will be the required amount of real mathematical content, hopefully.

My real goal is to answer question 3.  It's almost certainly ill-posed, and we will need to rethink what probability even means in the first place to answer this.  However, the answer is probably 0.