show/hide this revision's text 2 Duh, I meant 2^n vertices.

I believe the answer is "no"; the best known constructions only give no clique or independent set of size about 2^\sqrt{n} in a graph with n 2^n vertices. Bill Gasarch has a page on the subject here, although I don't know how frequently it updates.

show/hide this revision's text 1

I believe the answer is "no"; the best known constructions only give no clique or independent set of size about 2^\sqrt{n} in a graph with n vertices. Bill Gasarch has a page on the subject here, although I don't know how frequently it updates.