Minimal percolating sets in bootstrap percolation
| dc.creator | Morris, Robert | |
| dc.date | 2007-02-13 | |
| dc.date | 2008-10-14 | |
| dc.date.accessioned | 2026-07-07T10:09:41Z | |
| dc.date.available | 2026-07-07T10:09:41Z | |
| dc.description | 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. | |
| dc.description | 19 pgs, 4 figures, thorough rewrite, to appear in Electronic J. Combinatorics | |
| dc.identifier | https://arxiv.org/abs/math/0702370 | |
| dc.identifier | http://arxiv.org/abs/math/0702370 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/171395 | |
| dc.subject | Combinatorics | |
| dc.title | Minimal percolating sets in bootstrap percolation | |
| dc.type | text |