منابع مشابه
Saturation in the Hypercube and Bootstrap Percolation
Let Qd denote the hypercube of dimension d. Given d ≥ m, a spanning subgraph G of Qd is said to be (Qd, Qm)-saturated if it does not contain Qm as a subgraph but adding any edge of E(Qd) \E(G) creates a copy of Qm in G. Answering a question of Johnson and Pinto [27], we show that for every fixed m ≥ 2 the minimum number of edges in a (Qd, Qm)-saturated graph is Θ(2 d). We also study weak satura...
متن کاملMajority Bootstrap Percolation on the Hypercube
In majority bootstrap percolation on a graph G, an infection spreads according to the following deterministic rule: if at least half of the neighbours of a vertex v are already infected, then v is also infected, and infected vertices remain infected forever. Percolation occurs if eventually every vertex is infected. The elements of the set of initially infected vertices, A ⊂ V (G), are normally...
متن کاملA survey of dynamical percolation
Percolation is one of the simplest and nicest models in probability theory/statistical mechanics which exhibits critical phenomena. Dynamical percolation is a model where a simple time dynamics is added to the (ordinary) percolation model. This dynamical model exhibits very interesting behavior. Our goal in this survey is to give an overview of the work in dynamical percolation that has been do...
متن کاملExtremal bounds for bootstrap percolation in the hypercube
The r-neighbour bootstrap process on a graph G starts with an initial set A0 of “infected” vertices and, at each step of the process, a healthy vertex becomes infected if it has at least r infected neighbours (once a vertex becomes infected, it remains infected forever). If every vertex of G eventually becomes infected, then we say that A0 percolates. We prove a conjecture of Balogh and Bollobá...
متن کاملAccessibility percolation and first-passage site percolation on the unoriented binary hypercube
Inspired by biological evolution, we consider the following socalled accessibility percolation problem: The vertices of the unoriented ndimensional binary hypercube are assigned independent U(0, 1) weights, referred to as fitnesses. A path is considered accessible if fitnesses are strictly increasing along it. We prove that the probability that the global fitness maximum is accessible from the ...
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: Metrika
سال: 2013
ISSN: 0026-1335,1435-926X
DOI: 10.1007/s00184-013-0473-5