Let t be an integer such that $t\ge 2$. Let $K_{2,t}^{(3)}$ denote the triple system consisting of the 2t triples $\{a,x_i,y_i\}$, $\{b,x_i,y_i\}$ for $1\le i\le t$, where the elements $a,b,x_1,x_2,\dots ,x_t$, $y_1,y_2,\dots ,y_t$ are all distinct. Let $\mathrm{ex}(n,K_{2,t}^{(3)})$ denote the maximum size of a triple system on n elements that does not contain $K_{2,t}^{(3)}$. This function was studied by Mubayi and Verstraëte [9], where the special case $t=2$ was a problem of Erdős [1] that was studied by various authors [3], [9], [10].

Mubayi and Verstraëte proved that $\mathrm{ex}(n,K_{2,t}^{(3)})<t^4\left(\begin{array}{c}n\\ 2\end{array}\right)$ and that for infinitely many n, $\mathrm{ex}(n,K_{2,t}^{(3)})\ge \frac{2t-1}{3}\left(\begin{array}{c}n\\ 2\end{array}\right)$. These bounds together with a standard argument show that $g(t):={\lim }_{n\to \infty }\mathrm{ex}(n,K_{2,t}^{(3)})/\left(\begin{array}{c}n\\ 2\end{array}\right)$ exists and that$\frac{2t-1}{3}\le g(t)\le t^4.$ Addressing the question of Mubayi and Verstraëte on the growth rate of $g(t)$, we prove that as $t\to \infty$,$g(t)=\mathrm{\Theta }(t^{1+o(1)}).$

令t为一个整数，使得$Ť\ge 2$。让${ķ}_{2，Ť}^{（3）}$表示由2 t三元组组成的三元组系统$\{\mathrm{一种}，X_{\mathrm{一世}}，{ÿ}_{\mathrm{一世}}\}$， $\{b，X_{\mathrm{一世}}，{ÿ}_{\mathrm{一世}}\}$ 对于 $\mathrm{1个}\le \mathrm{一世}\le Ť$，其中的元素 $\mathrm{一种}，b，X_{\mathrm{1个}}，X_2，\dots ，X_{Ť}$， ${ÿ}_{\mathrm{1个}}，{ÿ}_2，\dots ，{ÿ}_{Ť}$都是截然不同的。让$\mathrm{前}（ñ，{ķ}_{2，Ť}^{（3）}）$表示不包含n个元素的三元系统的最大大小${ķ}_{2，Ť}^{（3）}$。Mubayi和Verstraëte[9]研究了此功能，其中特例$Ť=2$ 是Erdős[1]的问题，已被多位作者[3]，[9]，[10]研究。

Mubayi和Verstraëte证明了 $\mathrm{前}（ñ，{ķ}_{2，Ť}^{（3）}）<{Ť}^4（\begin{array}{c}ñ\\ 2\end{array}）$并且对于无穷多个ñ，$\mathrm{前}（ñ，{ķ}_{2，Ť}^{（3）}）\ge \frac{2Ť-\mathrm{1个}}{3}（\begin{array}{c}ñ\\ 2\end{array}）$。这些界限与标准参数一起表明$G（Ť）：={\mathrm{林}}_{ñ\to \infty }\mathrm{前}（ñ，{ķ}_{2，Ť}^{（3）}）/（\begin{array}{c}ñ\\ 2\end{array}）$ 存在，那$\frac{2Ť-\mathrm{1个}}{3}\le G（Ť）\le {Ť}^4。$ 解决穆巴伊和韦斯特拉特的增长率问题 $G（Ť）$，我们证明 $Ť\to \infty$，$G（Ť）=\mathrm{\Theta }（{Ť}^{\mathrm{1个}+Ø（\mathrm{1个}）}）。$