论文标题
Turán定理的确切稳定性
Exact stability for Turán's Theorem
论文作者
论文摘要
Turán的定理说，极好的$ k_ {r+1} $ - 免费图是$ r $ - 明确图。 ERDőS和Simonovits的稳定性定理表明，如果$ k_ {r+1} $ - 带有$ n $ VERTICES的免费图形接近最大$ t_r（n）$ edges，则接近$ r $ $ $ - 优点。在本文中，我们准确确定$ k_ {r+1} $ - 至少$ m $边缘的免费图形，与$ r $ - 分支最远，对于任何$ m \ ge t_r（n） - δ_rn^2 $。这扩展了Erdős，Győri和Simonovits的工作，并证明了Balogh，Clemen，Lavrov，Lidický和Pfender的猜想。
Turán's Theorem says that an extremal $K_{r+1}$-free graph is $r$-partite. The Stability Theorem of Erdős and Simonovits shows that if a $K_{r+1}$-free graph with $n$ vertices has close to the maximal $t_r(n)$ edges, then it is close to being $r$-partite. In this paper we determine exactly the $K_{r+1}$-free graphs with at least $m$ edges that are farthest from being $r$-partite, for any $m\ge t_r(n) - δ_r n^2$. This extends work by Erdős, Győri and Simonovits, and proves a conjecture of Balogh, Clemen, Lavrov, Lidický and Pfender.
