Bootstrap percolation on G(n,p) revisited
arXiv:1605.02995
Abstract
Bootstrap percolation on a graph with infection threshold is an infection process, which starts from a set of initially infected vertices and in each step every vertex with at least infected neighbours becomes infected. We consider bootstrap percolation on the binomial random graph , which was investigated among others by Janson, Łuczak, Turova and Valier (2012). We improve their results by strengthening the probability bounds for the number of infected vertices at the end of the process.
12 pages, to appear in Proceedings of the 27th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms, Krakow, Poland, 4-8 July 2016