European Journal of Combinatorics ( IF 1.0 ) Pub Date : 2020-08-20 , DOI: 10.1016/j.ejc.2020.103207 Sean English , Calum MacRury , Paweł Prałat
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 when we start with a single vertex colored blue. We show that when , then with high probability it takes rounds for all the vertices in to become blue, and when , then with high probability it takes rounds.
中文翻译:
随机图上的概率零强迫
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 当我们从蓝色的单个顶点开始时。我们证明了,那么很有可能 舍入为所有顶点 变成蓝色,何时 ,那么很有可能 回合。