Contagious sets in random graphs
نویسندگان
چکیده
منابع مشابه
Contagious Sets in Random Graphs
We consider the following activation process in undirected graphs: a vertex is active either if it belongs to a set of initially activated vertices or if at some point it has at least 2 active neighbors. A contagious set is a set whose activation results with the entire graph being active. Given a graph G, let m(G, 2) be the minimal size of a contagious set. We consider the binomial random grap...
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We consider the following activation process in undirected graphs: a vertex is active either if it belongs to a set of initially activated vertices or if at some point it has at least r active neighbors. A contagious set is a set whose activation results with the entire graph being active. Given a graph G, let m(G, r) be the minimal size of a contagious set. We study this process on the binomia...
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We study the activation process in undirected graphs known as bootstrap percolation: a vertex is active either if it belongs to a set of initially activated vertices or if at some point it had at least r active neighbors, for a threshold r that is identical for all vertices. A contagious set is a vertex set whose activation results with the entire graph being active. Let m(G, r) be the size of ...
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We consider the following activation process in d-regular undirected graphs: a vertex is active either if it belongs to a set of initially activated vertices or if at some point it has at least r active neighbors, where 1 < r ≤ d is the activation threshold. Such processes have been studied extensively in several fields such as combinatorics, computer science, probability and statistical physic...
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ژورنال
عنوان ژورنال: The Annals of Applied Probability
سال: 2017
ISSN: 1050-5164
DOI: 10.1214/16-aap1254