Strong-majority bootstrap percolation on regular graphs with low dissemination threshold

Dieter Mitsche, Xavier Pérez-Giménez and Paweł Prałat

Stochastic Processes and their Applications, 2017, vol. 127, issue 9, 3110-3134

Abstract: Consider the following model of strong-majority bootstrap percolation on a graph. Let r≥1 be some integer, and p∈[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).

Keywords: Bootstrap percolation; Regular graphs; Strong majority rule (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1016/j.spa.2017.02.001

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