منابع مشابه
Contagious 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 کاملNew Bounds on Cap Sets
The problem of the maximal size of cap sets is a characteristic 3 model for the problem of finding arithmetic progressions of length 3 in rather dense sets of integers. Meshulam [M95] , through a direct use of ideas of Roth, was able to show that there is a constant C so that any cap set A has density at most C N . Our result may be viewed as a very modest improvement over Meshulam’s result. Sa...
متن کاملContagious 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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2012
ISSN: 0012-365X
DOI: 10.1016/j.disc.2012.01.016