For two graphs $G$ and $F$, the extremal number of $F$ in $G$, denoted by {ex}$(G,F)$, is the maximum number of edges in a spanning subgraph of $G$ not containing $F$ as a subgraph. Determining {ex}$(K_n,F)$ for a given graph $F$ is a classical extremal problem in graph theory. In 1962, Erd\H{o}s determined {ex}$(K_n,kK_3)$, which generalized Mantel's Theorem. On the other hand, in 1974, {Bollob\'{a}s}, Erd\H{o}s, and Straus determined {ex}$(K_{n_1,n_2,\dots,n_r},K_t)$, which extended Tur\'{a}n's Theorem to complete multipartite graphs. { In this paper,} we determine {ex}$(K_{n_1,n_2,\dots,n_r},kK_3)$ for $r\ge 4$ and $10k-4\le n_1+4k\le n_2\le n_3\le \cdots \le n_r$.

翻译：对于两个图$G$和$F$，$F$在$G$中的极值数，记为{ex}$(G,F)$，是指$G$的不包含$F$作为子图的生成子图的最大边数。对于给定图$F$，确定{ex}$(K_n,F)$是图论中的一个经典极值问题。1962年，Erdős确定了{ex}$(K_n,kK_3)$，这推广了Mantel定理。另一方面，1974年，Bollobás、Erdős和Straus确定了{ex}$(K_{n_1,n_2,\dots,n_r},K_t)$，将Turán定理推广到了完全多部图。本文中，我们确定了当$r\ge 4$且$10k-4\le n_1+4k\le n_2\le n_3\le \cdots \le n_r$时，{ex}$(K_{n_1,n_2,\dots,n_r},kK_3)$的值。