We study the uniqueness of optimal solutions to extremal graph theory
problems. Lovasz conjectured that every finite feasible set of subgraph density
constraints can be extended further by a finite set of density constraints so
that the resulting set is satisfied by an asymptotically unique graph. This
statement is often referred to as saying that `every extremal graph theory
problem has a finitely forcible optimum'. We present a counterexample to the
conjecture. Our techniques also extend to a more general setting involving
other types of constraints
