Majority Bootstrap Percolation on $G(n,p)$

Cecilia Holmgren; Tomas Juškevičius; Nathan Kettle

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arXiv · 1508.02671

Majority Bootstrap Percolation on $G(n,p)$

Cecilia Holmgren·Tomas Juškevičius·Nathan Kettle

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Abstract

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 more infected than non-infected neighbours are infected. We say that percolation occurs if eventually all vertices in $G$ become infected. In this paper we study majority bootstrap percolation on the Erd\H{o}s-R\'enyi random graph $G(n,p)$ above the connectivity threshold. Perhaps surprisingly, the results obtained for small $p$ are comparable to the results for the hypercube obtained by Balogh, Bollob\'as and Morris (2009).

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BibTeX RIS

Cecilia Holmgren, Tomas Juškevičius, Nathan Kettle. 2015-08-11. Majority Bootstrap Percolation on $G(n,p)$. https://arxiv.org/abs/1508.02671

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