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Paper   IPM / M / 16456
School of Mathematics
  Title:   On K2,t-bootstrap percolation
1.  Mohammadreza Bidgoli
2.  Behruz Tayfeh-Rezaie (Joint with A. Mohammadian)
  Status:   To Appear
  Journal: Graphs Combin.
  Supported by:  IPM
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 Erdös-Rényi model for the complete graph H and proposed the similar problem for H=Ks,t, the complete bipartite graph. In this paper, we provide lower and upper bounds on the threshold of K2, t-bootstrap percolation. In addition, a threshold function is derived for K2, 4-bootstrap percolation.

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