A survey of Turán problems for expansions

关于书图扩张的Turán数

On the Turán number of the expansion of the book

该研究确定了充分大n时书图的3-扩张的Turán数，涉及书图、图的r-扩张及Turán数相关内容。

关于扩张的广义图论问题

On generalized Turán problems for expansions

本文研究了扩张的广义图论问题，确定了完全图扩张的精确广义图论数，并研究了多种森林类别的扩张的渐进行为。

关于 $t$-扇扩张的 Turán 数

On the Turán number of the expansion of the $t$-fan

本文研究 $t$-扇图的 3-一致扩张超图，在顶点数 $n$ 充分大时确定其 Turán 数。

广义Turán问题综述——子图计数

Survey of generalized Turán problems -- counting subgraphs

本文综述了广义Turán数$\mathrm{ex}(n,H,F)$的研究，即在$n$顶点无$F$图中最大化子图$H$副本数的极值问题，系统梳理了自Alon和Shikhelman 2016年开创性工作以来的主要进展与成果。

超图展开的随机Turán问题

Random Turán Problems for Hypergraph Expansions

该研究首次系统性探究一般超图F的r-一致展开F^(r)的随机Turán问题，通过证明Sidorenko超图在r足够大时的三阶段行为及非Sidorenko展开的复杂性，本质解决大r情形问题，并统一推广已知退化超图结果。

Turan Problems and Shadows III: expansions of graphs

The expansion $G^+$ of a graph $G$ is the $3$-uniform hypergraph obtained from $G$ by enlarging each edge of $G$ with a new vertex disjoint from $V(G)$ such that distinct edges are enlarged by distinct vertices. Let $ex_3(n,F)$ denote the maximum number of edges in a $3$-uniform hypergraph with $n$ vertices not containing any copy of a $3$-uniform hypergraph $F$. The study of $ex_3(n,G^+)$ includes some well-researched problems, including the case that $F$ consists of $k$ disjoint edges, $G$ is a triangle, $G$ is a path or cycle, and $G$ is a tree. In this paper we initiate a broader study of …