广义Turán问题的一些稳定性和精确结果

IF 0.4 4区数学 Q4 MATHEMATICS

Studia Scientiarum Mathematicarum Hungarica 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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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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来源期刊

Studia Scientiarum Mathematicarum Hungarica 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The journal publishes original research papers on various fields of mathematics, e.g., algebra, algebraic geometry, analysis, combinatorics, dynamical systems, geometry, mathematical logic, mathematical statistics, number theory, probability theory, set theory, statistical physics and topology.