3 citations · 4 across the 2 of their papers we have counts for
5 papers
Smallest percolating sets in bootstrap percolation on grids
Michał Przykucki, Thomas Shelton
In this paper we fill in a fundamental gap in the extremal bootstrap percolation literature, by providing the first proof of the fact that for all , the size of the small…
On the maximum running time in graph bootstrap percolation
Béla Bollobás, Michał Przykucki, Oliver Riordan +1
Graph bootstrap percolation is a simple cellular automaton introduced by Bollobás in 1968. Given a graph and a set we initially "infect" all edges in a…
The time of graph bootstrap percolation
Karen Gunderson, Sebastian Koch, Michał Przykucki
Graph bootstrap percolation, introduced by Bollobás in 1968, is a cellular automaton defined as follows. Given a "small" graph and a "large" graph , in c…
Subcritical -bootstrap percolation models have non-trivial phase transitions
Paul Balister, Béla Bollobás, Michał Przykucki +1
We prove that there exist natural generalizations of the classical bootstrap percolation model on that have non-trivial critical probabilities, and moreover we chara…
Bootstrap percolation on Galton-Watson trees
Béla Bollobás, Karen Gunderson, Cecilia Holmgren +2
Bootstrap percolation is a type of cellular automaton which has been used to model various physical phenomena, such as ferromagnetism. For each natural number , the -neighbou…