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.

中文翻译：

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难以捉摸的极值图

我们研究极值图论问题的最优解的唯一性。Lovasz推测，子图密度约束的每个有限可行集都可以通过密度约束的有限集进一步扩展，以使渐近唯一图满足结果集。这种说法通常被称为“每个极值图论问题都有一个有限的强制最优”。我们提出了一个猜想的反例。我们的技术还扩展到涉及其他类型约束的更一般的设置。