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Bootstrap percolation is a process that is used to model the spread of an infection on a given graph. In the model considered here each vertex is equipped with an individual threshold. As soon as the number of infected neighbors exceeds…
The $r$-neighbour bootstrap process describes an infection process on a graph, where we start with a set of initially infected vertices and an uninfected vertex becomes infected as soon as it has $r$ infected neighbours. An inital set of…
The $r$-neighbor bootstrap percolation is a graph infection process based on the update rule by which a vertex with $r$ infected neighbors becomes infected. We say that an initial set of infected vertices propagates if all vertices of a…
The bootstrap percolation (or threshold model) is a dynamic process modelling the propagation of an epidemic on a graph, where inactive vertices become active if their number of active neighbours reach some threshold. We study an…
The $r$-neighbour bootstrap process is an update rule for the states of vertices in which `uninfected' vertices with at least $r$ `infected' neighbours become infected and a set of initially infected vertices is said to \emph{percolate} if…
The $r$-bond bootstrap percolation process on a graph $G$ begins with a set $S$ of infected edges of $G$ (all other edges are healthy). At each step, a healthy edge becomes infected if at least one of its endpoints is incident with at least…
In this paper we focus on $r$-neighbor bootstrap percolation, which is a process on a graph where initially a set $A_0$ of vertices gets infected. Now subsequently, an uninfected vertex becomes infected if it is adjacent to at least $r$…
Bootstrap percolation is a type of cellular automaton which has been used to model various physical phenomena, such as ferromagnetism. For each natural number $r$, the $r$-neighbour bootstrap process is an update rule for vertices of a…
Bootstrap percolation in (random) graphs is a contagion dynamics among a set of vertices with certain threshold levels. The process is started by a set of initially infected vertices, and an initially uninfected vertex with threshold $k$…
Bootstrap percolation is a type of cellular automaton on graphs, introduced as a simple model of the dynamics of ferromagnetism. Vertices in a graph can be in one of two states: `healthy' or `infected' and from an initial configuration of…
Bootstrap Percolation is a process defined on a graph which begins with an initial set of infected vertices. In each subsequent round, an uninfected vertex becomes infected if it is adjacent to at least $r$ previously infected vertices. If…
Bootstrap percolation on a graph with infection threshold $r\in \mathbb{N}$ is an infection process, which starts from a set of initially infected vertices and in each step every vertex with at least $r$ infected neighbours becomes…
A bootstrap percolation process on a graph $G$ is an "infection" process which evolves in rounds. Initially, there is a subset of infected nodes and in each subsequent round each uninfected node which has at least $r$ infected neighbours…
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…
In this work we investigate a bootstrap percolation process on random graphs generated by a random graph model which combines preferential attachment and edge insertion between previously existing vertices. The probabilities of adding…
The theme of this paper is the analysis of bootstrap percolation processes on random graphs generated by preferential attachment. This is a class of infection processes where vertices have two states: they are either infected or…
Graph bootstrap percolation is a discrete-time process capturing the spread of a virus on the edges of $K_n$. Given an initial set $G\subseteq K_n$ of infected edges, the transmission of the virus is governed by a fixed graph $H$: in each…
In r-neighbour bootstrap percolation on a graph G, a set of initially infected vertices A \subset V(G) is chosen independently at random, with density p, and new vertices are subsequently infected if they have at least r infected…
For $r\geq1$, the $r$-neighbour bootstrap process in a graph $G$ starts with a set of infected vertices and, in each time step, every vertex with at least $r$ infected neighbours becomes infected. The initial infection percolates if every…
Bootstrap percolation is a prominent framework for studying the spreading of activity on a graph. We begin with an initial set of active vertices. The process then proceeds in rounds, and further vertices become active as soon as they have…