Majority bootstrap percolation on a graph $G$ is an epidemic process defined in the following manner. Firstly, an initially infected set of vertices is selected. Then step by step the vertices that have at least half of its neighbours infected become infected. We say that percolation occurs if eventually all vertices in $G$ become infected.In this paper we provide sharp bounds for the critical size of the initially infected set in majority bootstrap percolation on the Erdős-Rényi random graph $G(n,p)$. This answers an open question by Janson, Luczak, Turova and Vallier (2012). Our results obtained for $p=c\log(n)/n$ are close to the results obtained by Balogh, Bollobás and Morris (2009) for majority bootstrap percolation on the hypercube. We conjecture that similar results will be true for all regular-like graphs with the same density and sufficiently strong expansion properties.
@article{10_37236_6000,
author = {Cecilia Holmgren and Tomas Ju\v{s}kevi\v{c}ius and Nathan Kettle},
title = {Majority bootstrap percolation on {\(G(n,p)\)}},
journal = {The electronic journal of combinatorics},
year = {2017},
volume = {24},
number = {1},
doi = {10.37236/6000},
zbl = {1355.05226},
url = {http://geodesic.mathdoc.fr/articles/10.37236/6000/}
}
TY - JOUR
AU - Cecilia Holmgren
AU - Tomas Juškevičius
AU - Nathan Kettle
TI - Majority bootstrap percolation on \(G(n,p)\)
JO - The electronic journal of combinatorics
PY - 2017
VL - 24
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/6000/
DO - 10.37236/6000
ID - 10_37236_6000
ER -
%0 Journal Article
%A Cecilia Holmgren
%A Tomas Juškevičius
%A Nathan Kettle
%T Majority bootstrap percolation on \(G(n,p)\)
%J The electronic journal of combinatorics
%D 2017
%V 24
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/6000/
%R 10.37236/6000
%F 10_37236_6000
Cecilia Holmgren; Tomas Juškevičius; Nathan Kettle. Majority bootstrap percolation on \(G(n,p)\). The electronic journal of combinatorics, Tome 24 (2017) no. 1. doi: 10.37236/6000
