Minimal Percolating Sets in Bootstrap Percolation
نویسنده
چکیده
In standard bootstrap percolation, a subset A of the grid [n] 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/33 + o(n), but there does not exist one larger than (n + 2)/6.
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ورودعنوان ژورنال:
- Electr. J. Comb.
دوره 16 شماره
صفحات -
تاریخ انتشار 2009