The notion of weak saturation was introduced by Bollobás in 1968. Let F and H be graphs. A spanning subgraph $G\subseteq F$ is weakly $(F,H)$-saturated if it contains no copy of H but there exists an ordering $e_1,\dots ,e_t$ of $E(F)\setminus E(G)$ such that for each $i\in [t]$, the graph $G\cup \{e_1,\dots ,e_i\}$ contains a copy $H^{\prime }$ of H such that $e_i\in H^{\prime }$. Define $\mathrm{wsat}(F,H)$ to be the minimum number of edges in a weakly $(F,H)$-saturated graph. In this paper, we prove for all $t\ge 2$ and $n\ge 3t-3$, that $\mathrm{wsat}(K_n,K_{t,t})=(t-1)(n+1-t/2)$, and we determine the value of $\mathrm{wsat}(K_n,K_{t-1,t})$ as well. For fixed $2\le s<t$, we also obtain bounds on $\mathrm{wsat}(K_n,K_{s,t})$ that are asymptotically tight.

弱饱和度的概念由Bollobás于1968年提出。令F和H为图。跨子图$G\subseteq F$是弱 $（F，H）$-饱和，如果它不包含H的副本但存在一个排序${Ë}_{\mathrm{1个}}，\dots ，{Ë}_{Ť}$ 的 $Ë（F）\setminus Ë（G）$ 这样每个 $\mathrm{一世}\in [Ť]$，图 $G\cup \{{Ë}_{\mathrm{1个}}，\dots ，{Ë}_{\mathrm{一世}}\}$ 包含副本 $H^{\prime }$的ħ使得${Ë}_{\mathrm{一世}}\in H^{\prime }$。定义$\mathrm{at}（F，H）$ 成为弱点中的最小边数 $（F，H）$-饱和图。在本文中，我们为所有人证明$Ť\ge 2$ 和 $ñ\ge 3Ť-3$， $\mathrm{at}（{ķ}_{ñ}，{ķ}_{Ť，Ť}）=（Ť-\mathrm{1个}）（ñ+\mathrm{1个}-Ť/2）$，我们确定 $\mathrm{at}（{ķ}_{ñ}，{ķ}_{Ť-\mathrm{1个}，Ť}）$也一样 对于固定$2\le s<Ť$，我们还获得了 $\mathrm{at}（{ķ}_{ñ}，{ķ}_{s，Ť}）$ 渐近地紧。