Abstract
Bootstrap percolation was introduced by Chalupa, Leath and Reich [6] during the 1970’s in the context of magnetic disordered systems and has been re-discovered since then by several authors mainly due to its connections with various physical models. A bootstrap percolation process with activation threshold an integer r ≥ 2 on a graph G = G(V, E) is a deterministic process which evolves in rounds. Every vertex has two states: it is either infected or uninfected. Initially, there is a subset A 0 ⊆ V which consists of infected vertices, whereas every other vertex is uninfected. Subsequently, in each round, if an uninfected vertex has at least r of its neighbours infected, then it also becomes infected and remains so forever. This is repeated until no more vertices become infected. We denote the final infected set by A f . Our general assumption will be that the initial set of infected vertices A 0 is chosen randomly among all subsets of vertices of a certain size.
This research has been supported by the EPSRC Grant EP/K019740/1.
The author was partially supported by DFG grant PA 2080/1.
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Amini, H., Fountoulakis, N., Panagiotou, K. (2013). Discontinuous bootstrap percolation in power-law random graphs. In: Nešetřil, J., Pellegrini, M. (eds) The Seventh European Conference on Combinatorics, Graph Theory and Applications. CRM Series, vol 16. Edizioni della Normale, Pisa. https://doi.org/10.1007/978-88-7642-475-5_69
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DOI: https://doi.org/10.1007/978-88-7642-475-5_69
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