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Paper IPM / M / 16456  


Abstract:  
Given two graphs G and H, it is said that G percolates in Hbootstrap 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 Hbootstrap percolation in the ErdösRényi 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.
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