  We characterize f-vectors of sufficiently large three-dimensional flag
Gorenstein* complexes, essentially confirming a conjecture of Gal [Discrete
Comput. Geom., 34 (2), 269--284, 2005]. In particular, this characterizes
f-vectors of large flag triangulations of the 3-sphere. Actually, our main
result is more general and describes the structure of closed flag 3-manifolds
which have many edges.
  Looking at the 1-skeleta of these manifolds we reduce the problem to a
certain question in extremal graph theory. We then resolve this question by
employing the Supersaturation Theorem of Erdos and Simonovits.
