Thanks for pointing this out! I've always wondered if determining the exact value for all bipartite graphs would give the exact result for all graphs, and I certainly wasn't aware of this result (any more info on where I could find it?). I often hear things like "Erdos-Stone gives us the correct asymptotics for non-bipartite graphs," but I think it would be better to say something like "Erdos-Stone gives the correct asymptotics for all graphs, but says nothing about the lower order terms for any graph. It just so happens that for bipartite graphs the lower order terms are all there is."

You are right in your assumption; I don't have a topic in mind yet. I am open to anything as long as it is within the realm of graph theory/combinatorics.

I'm thinking there may be 20 people although I don't know for sure. This include students and other faculty who may be at the picnic.