Geodesic
Minimal percolating sets in bootstrap percolation
The electronic journal of combinatorics, Tome 16 (2009) no. 1
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In standard bootstrap percolation, a subset $A$ of the grid $[n]^2$ is initially infected. A new site is then infected if at least two of its neighbours are infected, and an infected site stays infected forever. The set $A$ is said to percolate if eventually the entire grid is infected. A percolating set is said to be minimal if none of its subsets percolate. Answering a question of Bollobás, we show that there exists a minimal percolating set of size $4n^2/33 + o(n^2)$, but there does not exist one larger than $(n + 2)^2/6$.
DOI : 10.37236/91
Classification : 60K35 
@article{10_37236_91,
     author = {Robert Morris},
     title = {Minimal percolating sets in bootstrap percolation},
     journal = {The electronic journal of combinatorics},
     year = {2009},
     volume = {16},
     number = {1},
     doi = {10.37236/91},
     zbl = {1178.60070},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/91/}
}
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Robert Morris. Minimal percolating sets in bootstrap percolation. The electronic journal of combinatorics, Tome 16 (2009) no. 1. doi: 10.37236/91

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