AI 中文总结
该研究构造了满足特定条件的有限禁用子图族，证明其极值图无三因子乘积结构，对Simonovits乘积猜想相关问题给出否定答案。
AI 中文摘要
我们构造了一个固定的有限普通禁用子图族$\u2112$，满足$p(\u2112)=3$，且存在常数$c>0$，使得对所有足够大的阶数$n$，均有$ex(n,\u2112)>t_3(n)+cn^{3/2}$。然而，每个足够大的$\u2112$-极值图的补图最多有两个连通分量，即不存在此类极值图是三个正阶图的完全联。这对源于Simonovits乘积猜想的一个仅询问每个足够大阶数是否存在一个乘积极值器的自然存在性问题给出了否定答案。
英文摘要
We construct a fixed finite family $\mathcal L$ of ordinary forbidden subgraphs with $p(\mathcal L)=3$ and a constant $c>0$ such that $$ex(n,\mathcal L)>t_3(n)+cn^{3/2}$$ at every sufficiently large order. Nevertheless, the complement of every sufficiently large $\mathcal L$-extremal graph has at most two connected components. In particular, no such extremal graph is a complete join of three graphs of positive order. This gives a negative answer to a natural existence-only question motivated by the Simonovits Product Conjecture, in which one asks only for one product extremizer at each sufficiently large order.
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