منابع مشابه
Contagious Sets in Dense Graphs
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 ...
متن کاملContagious 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...
متن کاملProbability 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 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...
متن کاملContagious Sets in Expanders
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...
متن کاملStrength of strongest dominating sets in fuzzy graphs
A set S of vertices in a graph G=(V,E) is a dominating set ofG if every vertex of V-S is adjacent to some vertex of S.For an integer k≥1, a set S of vertices is a k-step dominating set if any vertex of $G$ is at distance k from somevertex of S. In this paper, using membership values of vertices and edges in fuzzy graphs, we introduce the concepts of strength of strongestdominating set as well a...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2018
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2017.07.011