Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5130038 | Stochastic Processes and their Applications | 2017 | 25 Pages |
Abstract
Consider the following model of strong-majority bootstrap percolation on a graph. Let râ¥1 be some integer, and pâ[0,1]. Initially, every vertex is active with probability p, independently from all other vertices. Then, at every step of the process, each vertex v of degree deg(v) becomes active if at least (deg(v)+r)/2 of its neighbours are active. Given any arbitrarily small p>0 and any integer r, we construct a family of d=d(p,r)-regular graphs such that with high probability all vertices become active in the end. In particular, the case r=1 answers a question and disproves a conjecture of Rapaport et al. (2011).
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Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Dieter Mitsche, Xavier Pérez-Giménez, PaweÅ PraÅat,