论文标题
$ k $的极端图 - 路径的力量
Extremal graphs of the $k$-th power of paths
论文作者
论文摘要
给定图形$ h $的极端图是一个图形，在固定数量的顶点上具有最大边缘数，而无需包含$ h $的副本。路径的$ k $ th功率是从路径获得的图形，并将路径的所有对顶点连接起来，距离小于$ k $。应用Simonovits的深度定理，我们表征了$ k $ th的路径功率的极端图。这解决了Xiao，Katona，Xiao和Zamora提出的猜想，形式更强。
An extremal graph for a given graph $H$ is a graph with maximum number of edges on fixed number of vertices without containing a copy of $H$. The $k$-th power of a path is a graph obtained from a path and joining all pair of vertices of the path with distance less than $k$. Applying a deep theorem of Simonovits, we characterize the extremal graphs of the $k$-th power of paths. This settles a conjecture posed by Xiao, Katona, Xiao and Zamora in a stronger form.
