منابع مشابه
The time of graph bootstrap percolation
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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Bootstrap percolation on the random graph Gn,p is a process of spread of “activation” on a given realization of the graph with a given number of initially active nodes. At each step those vertices which have not been active but have at least r ≥ 2 active neighbours become active as well. We study the size A∗ of the final active set. The parameters of the model are, besides r (fixed) and n (tend...
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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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Graph bootstrap percolation is a deterministic cellular automaton which was introduced by Bollobás in 1968, and is defined as follows. Given a graph H, and a set G ⊂ E(K n) of initially 'infected' edges, we infect, at each time step, a new edge e if there is a copy of H in K n such that e is the only not-yet infected edge of H. We say that G percolates in the H-bootstrap process if eventually e...
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We study a variant of bootstrap percolation in which growth is restricted to a single active cluster. Initially there is a single active site at the origin, while other sites of Z2 are independently occupied with small probability p, otherwise empty. Subsequently, an empty site becomes active by contact with two or more active neighbors, and an occupied site becomes active if it has an active s...
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ژورنال
عنوان ژورنال: Random Structures & Algorithms
سال: 2012
ISSN: 1042-9832
DOI: 10.1002/rsa.20458