Find the number of undirected graphs on vertices such that, whenever there is a path joining the vertices , then there is a complete graph on .
I can't think of any hints that wouldn't be completely and utterly cryptic, so I'll just sort of give you the logical leap bit, and is hopefully only a wee bit cryptic...presuming, of course, you didn't quite get the leap bit...
Basically, what you want to do find out how many ways there are of partitioning and n-element set.
I'm sure you can solve the problem from there.