Minimum Degree Conditions for Small Percolating Sets in Bootstrap Percolation
Minimum Degree Conditions for Small Percolating Sets in Bootstrap Percolation
The $r$-neighbour bootstrap process is an update rule for the states of vertices in which `uninfected' vertices with at least $r$ `infected' neighbours become infected and a set of initially infected vertices is said to percolate if eventually all vertices are infected. For every $r \geq 3$, a sharp condition …