论文标题
多目标图的稳定定理
A stability theorem for multi-partite graphs
论文作者
论文摘要
ERDőS-Simonovits稳定性定理是极端图理论中使用的最广泛使用的定理之一。我们在多目标图中获得了ERDőS-Simonovits类型稳定性定理。与ERDőS-Simonovits稳定性定理不同，我们在多目标图中的稳定性定理说，如果$ h $ free Graph $ g $的边数与$ H $的极端图接近$ H $，那么$ g $，那么$ g $具有明确的结构，但可能与$ h $相距较远。作为一个应用程序，我们解决了Han和Zhao提出的猜想，该猜想是关于多方图中最大边数的数量
The Erdős-Simonovits stability theorem is one of the most widely used theorems in extremal graph theory. We obtain an Erdős-Simonovits type stability theorem in multi-partite graphs. Different from the Erdős-Simonovits stability theorem, our stability theorem in multi-partite graphs says that if the number of edges of an $H$-free graph $G$ is close to the extremal graphs for $H$, then $G$ has a well-defined structure but may be far away to the extremal graphs for $H$. As an application, we solve a conjecture posed by Han and Zhao concerning the maximum number of edges in multi-partite graphs which does not contain vertex-disjoint copies of a clique
