广义Turán问题的一些稳定性和精确结果

Pub Date : 2022-04-10 DOI:10.1556/012.2023.01533

Dániel Gerbner

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引用次数: 9

摘要

给定图H和图F，广义的Turán数ex(n, H, F)是n顶点无F图中H的最大拷贝数。稳定性指的是一种常见的现象，如果一个n顶点无F的图G包含几乎ex(n, H, F)个H的副本，那么G在某种意义上类似于某个极值图。得到了广义Turán问题的新的稳定性结果，并得到了几个新的精确结果。

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Some Stability and Exact Results in Generalized Turán Problems

Given graphs H and F, the generalized Turán number ex(n, H, F) is the largest number of copies of H in n-vertex F-free graphs. Stability refers to the usual phenomenon that if an n-vertex F-free graph G contains almost ex(n, H, F) copies of H, then G is in some sense similar to some extremal graph. We obtain new stability results for generalized Turán problems and derive several new exact results.

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