On the Maximum Running Time in Graph Bootstrap Percolation
نویسندگان
چکیده
منابع مشابه
On the Maximum Running Time in Graph Bootstrap Percolation
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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Abstract: Graph bootstrap percolation, introduced by Bollobás in 1968, is a cellular automaton defined as follows. Given a “small” graph H and a “large” graph G = G0 ⊆ Kn, in consecutive steps we obtain Gt+1 from Gt by adding to it all new edges e such that Gt ∪ e contains a new copy of H. We say that G percolates if for some t ≥ 0, we have Gt = Kn. ForH = Kr, the question about the size of the...
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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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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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In 2-neighborhood 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 neighbors become infected. Percolation occurs if eventually every vertex is infected. The maximum time t(G) is the maximum number of rounds needed to ev...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2017
ISSN: 1077-8926
DOI: 10.37236/5771