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arXiv · 1806.10425

On $K_{2,t}$-bootstrap percolation

M. R. Bidgoli·A. Mohammadian·B. Tayfeh-Rezaie
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Abstract

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.

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M. R. Bidgoli, A. Mohammadian, B. Tayfeh-Rezaie. 2018-06-27. On $K_{2,t}$-bootstrap percolation. https://arxiv.org/abs/1806.10425

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