Maximum Percolation Time in Two-Dimensional Bootstrap Percolation
نویسندگان
چکیده
منابع مشابه
Maximum Percolation Time in Two-Dimensional Bootstrap Percolation
We consider a classical model known as bootstrap percolation on the n×n square grid. To each vertex of the grid we assign an initial state, infected or healthy, and then in consecutive rounds we infect every healthy vertex that has at least 2 already infected neighbours. We say that percolation occurs if the whole grid is eventually infected. In this paper, contributing to a recent series of ex...
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Graph bootstrap percolation is a simple cellular automaton introduced by Bollobás in 1968. Given a graph H and a set G ⊆ E(Kn) we initially ‘infect’ all edges in G and then, in consecutive steps, we infect every e ∈ Kn that completes a new infected copy of H in Kn. We say that G percolates if eventually every edge in Kn is infected. The extremal question about the size of the smallest percolati...
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In 2-neighbourhood bootstrap percolation on a graph G, an infection spreads according to the following deterministic rule: infected vertices of G remain infected forever and in consecutive rounds healthy vertices with at least 2 already infected neighbours become infected. Percolation occurs if eventually every vertex is infected. In this paper, we are interested to calculate the maximal time t...
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ژورنال
عنوان ژورنال: SIAM Journal on Discrete Mathematics
سال: 2015
ISSN: 0895-4801,1095-7146
DOI: 10.1137/130941584