  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, Bollob\'as
and Morris in 2012 investigated the threshold of $H$-bootstrap percolation in
the Erd\H{o}s-R\'enyi 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.

Combinatorics