The existence of Steiner triple systems $\mathrm{STS}\left(n\right)$ of order $n$ containing no nontrivial subsystem is well known for every admissible $n$. We generalize this result in two ways. First we define the expander property of 3-uniform hypergraphs and show the existence of Steiner triple systems which are almost perfect expanders.

Next we define the strong and weak spreading properties of linear hypergraphs, and determine the minimum size of a linear triple system with these properties, up to a small constant factor. This property is strongly connected to the connectivity of the structure and of the so-called influence maximization. We also discuss how the results are related to Erdős’ conjecture on locally sparse $\mathrm{STS}$s, influence maximization, subsquare-free Latin squares and possible applications in finite geometry.

斯坦纳三重系统的存在 $\mathrm{STS}（ñ）$ 顺序 $ñ$ 众所周知，每个子系统都包含非平凡的子系统 $ñ$。我们用两种方法概括该结果。首先，我们定义3一致超图的扩张器性质，并证明Steiner三重系统的存在，它们几乎是完美的扩张器。

接下来，我们定义线性超图的强扩散特性和弱扩散特性，并确定具有这些特性的线性三重系统的最小尺寸，直至较小的恒定因子。该属性与结构的连通性以及所谓的影响最大化密切相关。我们还将讨论结果与Erdős关于局部稀疏的猜想如何相关$\mathrm{STS}$s，影响最大化，无亚平方的拉丁方以及在有限几何中的可能应用。