Zero forcing is a deterministic iterative graph coloring process in which vertices are colored either blue or white, and in every round, any blue vertices that have a single white neighbor force these white vertices to become blue. Here we study probabilistic zero forcing, where blue vertices have a non-zero probability of forcing each white neighbor to become blue.

We explore the propagation time for probabilistic zero forcing on the Erdős–Réyni random graph $\mathcal{G}(n,p)$ when we start with a single vertex colored blue. We show that when $p={log}^{-o\left(1\right)}n$, then with high probability it takes $(1+o\left(1\right)){log}_2{log}_{2}n$ rounds for all the vertices in $\mathcal{G}(n,p)$ to become blue, and when $logn∕n\ll p\le {log}^{-O\left(1\right)}n$, then with high probability it takes $\Theta (log(1∕p))$ rounds.

零强迫是确定性的迭代图着色过程，其中顶点被着色为蓝色或白色，并且在每一轮中，具有单个白色邻居的任何蓝色顶点都会迫使这些白色顶点变为蓝色。在这里，我们研究概率为零的强迫，其中蓝色顶点具有迫使每个白色邻居变为蓝色的非零概率。

我们在Erdős-Réyni随机图上探索概率零强迫的传播时间 $\mathcal{G}（ñ，p）$当我们从蓝色的单个顶点开始时。我们证明了$p={日志}^{-Ø（\mathrm{1个}）}ñ$，那么很有可能 $（\mathrm{1个}+Ø（\mathrm{1个}））{日志}_2{日志}_2ñ$ 舍入为所有顶点 $\mathcal{G}（ñ，p）$ 变成蓝色，何时 $日志ñ∕ñ\ll p\le {日志}^{-Ø（\mathrm{1个}）}ñ$，那么很有可能 $\Theta （日志（\mathrm{1个}∕p））$ 回合。