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Bootstrap percolation on homogeneous trees has 2 phase transitions
(SPRINGER, 2008)
We study the threshold theta bootstrap percolation model on the homogeneous tree with degree b + 1, 2 <= theta <= b, and initial density p. It is known that there exists a nontrivial critical value for p, which we call ...
Strict Majority Bootstrap Percolation in the r-wheel
(Elsevier, 2014)
In the strict Majority Bootstrap Percolation process each passive vertex v becomes active if at least [fórmula] of its neighbors are active (and thereafter never changes its state). We address the problem of finding graphs ...
Insights into bootstrap percolation: Its equivalence with k-core percolation and the giant component
(American Physical Society, 2019-02)
K-core and bootstrap percolation are widely studied models that have been used to represent and understand diverse deactivation and activation processes in natural and social systems. Since these models are considerably ...
Nucleation and growth in two dimensions
(John Wiley & Sons Inc, 2019-10-22)
We consider a dynamical process on a graph G, in which vertices are infected (randomly) at a rate which depends on the number of their neighbors that are already infected. This model includes bootstrap percolation and ...