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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…
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 every uninfected node which has at least r infected neighbours…
In $\HH$-bootstrap percolation, a set $A \subset V(\HH)$ of initially 'infected' vertices spreads by infecting vertices which are the only uninfected vertex in an edge of the hypergraph $\HH$. A particular case of this is the $H$-bootstrap…
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…
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 $r$…
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…
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…
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…
On a geometric model for complex networks (introduced by Krioukov et al.) we investigate the bootstrap percolation process. This model consists of random geometric graphs on the hyperbolic plane having $N$ vertices, a dependent version of…
Following Bradonji\'c and Saniee, we study a model of bootstrap percolation on the Gilbert random geometric graph on the $2$-dimensional torus. In this model, the expected number of vertices of the graph is $n$, and the expected degree of a…
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…
Given a hypergraph $\mathcal{H}$, the $\mathcal{H}$-bootstrap process starts with an initial set of infected vertices of $\mathcal{H}$ and, at each step, a healthy vertex $v$ becomes infected if there exists a hyperedge of $\mathcal{H}$ in…
We consider bootstrap percolation on the binomial random graph $G(n,p)$ with infection threshold $r\in \mathbb{N}$, an infection process which starts from a set of initially infected vertices and in each step every vertex with at least $r$…
The $r$-neighbour bootstrap percolation process on a graph $G$ starts with an initial set $A_0$ 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…
We investigate bootstrap percolation with infection threshold $r> 1$ on the binomial $k$-uniform random hypergraph $H_k(n,p)$ in the regime $n^{-1}\ll n^{k-2}p \ll n^{-1/r}$, when the initial set of infected vertices is chosen uniformly at…
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…
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…
In $r$-neighbor bootstrap percolation on the vertex set of a graph $G$, a set $A$ of initially infected vertices spreads by infecting, at each time step, all uninfected vertices with at least $r$ previously infected neighbors. When the…
We investigate the behaviour of $r$-neighbourhood bootstrap percolation on the binomial $k$-uniform random hypergraph $H_k(n,p)$ for given integers $k\geq 2$ and $r\geq 2$. In $r$-neighbourhood bootstrap percolation, infection spreads…