Graham's number, for one,
"is an upper bound on the solution to a certain problem [1] in Ramsey theory." http://en.wikipedia.org/w...raham%27s_number
[1] Consider an n-dimensional hypercube, and connect each pair of vertices to obtain a complete graph on 2^n vertices. Then colour each of the edges of this graph either red or blue.
What is the smallest value of n for which every such colouring contains at least one single-coloured 4-vertex planar complete subgraph?
Googol(plex) aren't too useful, besides descriptively. (A googol is
"astronomical", a googolplex is hyper-mega astronomical, etc.)