论文标题
统一的Turán问题和过饱和的统一方法
Unified approach to the generalized Turán problem and supersaturation
论文作者
论文摘要
在本文中，我们介绍了一种统一的方法，以解决图形理论的普遍性Turán问题和过饱和导致的结果。 Supustatration-extremal函数$ satex（n，f：m，g）$是可以拥有的$ g $ g $ a $ n $ vertex Graph的最少副本，其中至少包含$ f $ $ f $的$ m $副本。我们提出了一项调查，讨论了先前已知的结果，并获得了一些新的，主要关注证明方法，极端结构和相变现象。最后，我们指出了一些有关超图，尤其是Berge型结果的极端问题的关系。
In this paper we introduce a unifying approach to the generalized Turán problem and supersaturation results in graph theory. The supersaturation-extremal function $satex(n, F : m, G)$ is the least number of copies of a subgraph $G$ an $n$-vertex graph can have, which contains at least $m$ copies of $F$ as a subgraph. We present a survey, discuss previously known results and obtain several new ones focusing mainly on proof methods, extremal structure and phase transition phenomena. Finally we point out some relation with extremal questions concerning hypergraphs, particularly Berge-type results.
