1. On K2,t-Bootstrap Percolation.
- Author
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Bidgoli, Mohammadreza, Mohammadian, Ali, and Tayfeh-Rezaie, Behruz
- Subjects
- *
PERCOLATION , *BIPARTITE graphs , *COMPLETE graphs , *RANDOM graphs - 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, 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. [ABSTRACT FROM AUTHOR]
- Published
- 2021
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