Given two graphs G and H, it is said that G percolates in H-bootstrap process if one could join all the nonadjacent pairs of vertices of G in some order such that a new copy of H is created at each step. Balogh, Bollobás and Morris in 2012 investigated the threshold of H-bootstrap percolation in the Erdős–Rényi model for the complete graph H and proposed the similar problem for \(H=K_{s,t}\), the complete bipartite graph. In this paper, we provide lower and upper bounds on the threshold of \(K_{2, t}\)-bootstrap percolation. In addition, a threshold function is derived for \(K_{2,4}\)-bootstrap percolation.

给定两个图G和H，如果一个G可以按某种顺序连接G的所有不相邻顶点对，从而在每个步骤中创建H的新副本，则可以说G在H -bootstrap过程中渗透。Balogh，Bollobás和Morris在2012年研究了完整图H的Erdős-Rényi模型中H引导渗滤的阈值，并提出了完整二部图\（H = K_ {s，t} \）的相似问题。在本文中，我们提供了\（K_ {2，t} \）- bootstrap渗滤阈值的上限和下限。此外，还导出了一个阈值函数，用于\（K_ {2,4} \）-引导渗透。