论文标题
用随机组零强迫
Zero Forcing with Random Sets
论文作者
论文摘要
给定图形$ g $和一个实数$ 0 \ le p \ le 1 $，我们通过独立包含每个顶点，并使用概率$ p $来定义随机集$ b_p（g）\ subset v（g）$。我们调查了随机集$ b_p（g）$是$ g $的零强迫集的可能性。特别是，我们证明，对于大$ n $，这种对树的概率受路径图的相应概率的上限。给定最小程度的条件，我们还证明了Boyer等人的猜想是关于图可以具有的给定尺寸的零强迫集数量的。
Given a graph $G$ and a real number $0\le p\le 1$, we define the random set $B_p(G)\subset V(G)$ by including each vertex independently and with probability $p$. We investigate the probability that the random set $B_p(G)$ is a zero forcing set of $G$. In particular, we prove that for large $n$, this probability for trees is upper bounded by the corresponding probability for a path graph. Given a minimum degree condition, we also prove a conjecture of Boyer et.\ al.\ regarding the number of zero forcing sets of a given size that a graph can have.
