Minimal percolating sets in bootstrap percolation

Details Minimal percolating sets in bootstrap percolation Minimal percolating sets in bootstrap percolation

2007-02-13

arxiv.org/abs/math/0702370v2

Mathematics

Combinatorics

19 pgs, 4 figures, thorough rewrite, to appear in Electronic J. Combinatorics

Scientific paper

In standard bootstrap percolation, a subset A of the n x n grid 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 Bollobas, 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.

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