Related papers: Burning rooted graph products
We study a discrete-time model for the spread of information in a graph, motivated by the idea that people believe a story when they learn of it from two different origins. Similar to the burning number, in this problem, information spreads…
The burning number of a graph $G$ is the smallest positive integer $k$ such that the vertex set of $G$ can be covered with balls of radii $0, 1, \dots, k-1$. A well-known conjecture by Bonato, Janssen and Roshabin states that any connected…
Graph burning is a process of information spreading through the network by an agent in discrete steps. The problem is to find an optimal sequence of nodes which have to be given information so that the network is covered in least number of…
Given a graph $G$, the optimization version of the graph burning problem seeks for a sequence of vertices, $(u_1,u_2,...,u_p) \in V(G)^p$, with minimum $p$ and such that every $v \in V(G)$ has distance at most $p-i$ to some vertex $u_i$.…
The burning process on a graph $G$ starts with a single burnt vertex, and at each subsequent step, burns the neighbors of the currently burnt vertices, as well as one other unburnt vertex. The burning number of $G$ is the smallest number of…
Graph burning is a deterministic, discrete-time process that models how influence or contagion spreads in a graph. Associated to each graph is its burning number, which is a parameter that quantifies how quickly the influence spreads. We…
The burning number of a graph $G$ is the smallest number $b$ such that the vertices of $G$ can be covered by balls of radii $0, 1, \dots, b-1$. As computing the burning number of a graph is known to be NP-hard, even on trees, it is natural…
The burning number of a graph can be used to measure the spreading speed of contagion in a network. The burning number conjecture is arguably the main unresolved conjecture related to this graph parameter, which can be settled by showing…
Consider an information diffusion process on a graph $G$ that starts with $k>0$ burnt vertices, and at each subsequent step, burns the neighbors of the currently burnt vertices, as well as $k$ other unburnt vertices. The \emph{$k$-burning…
Given a graph $G=(V, E)$, the problem of Graph Burning is to find a sequence of nodes from $V$, called a burning sequence, to burn the whole graph. This is a discrete-step process, and at each step, an unburned vertex is selected as an…
The burning number of a graph was recently introduced by Bonato et al. Although they mention that the burning number generalises naturally to directed graphs, no further research on this has been done. Here, we introduce graph burning for…
We introduce a new graph parameter called the burning number, inspired by contact processes on graphs such as graph bootstrap percolation, and graph searching paradigms such as Firefighter. The burning number measures the speed of the…
Burning and cooling are diffusion processes on graphs in which burned (or cooled) vertices spread to their neighbors with a new source picked at discrete time steps. In burning, the one tries to burn the graph as fast as possible, while in…
The burning number $b(G)$ of a graph $G$ was introduced by Bonato, Janssen, and Roshanbin [Lecture Notes in Computer Science 8882 (2014)] for measuring the speed of the spread of contagion in a graph. They proved for any connected graph $G$…
Given a graph $G$, the burning number of $G$ is the smallest integer $k$ for which there are vertices $x_1, x_2,\ldots,x_k$ such that $(x_1,x_2,\ldots,x_k)$ is a burning sequence of $G$. It has been shown that the graph burning problem is…
The graph burning problem is an NP-hard combinatorial optimization problem that helps quantify the vulnerability of a graph to contagion. This paper introduces a simple farthest-first traversal-based approximation algorithm for this problem…
We propose an exact algorithm for the Graph Burning Problem ($\texttt{GBP}$), an NP-hard optimization problem that models the spread of influence on social networks. Given a graph $G$ with vertex set $V$, the objective is to find a sequence…
Graph burning models the spread of information or contagion in a graph. At each time step, two events occur: neighbours of already burned vertices become burned, and a new vertex is chosen to be burned. The big conjecture is known as the…
Inspired by the spread of information in social networks and graph-theoretic processes such as Firefighting and graph cleaning, Bonato, Janssen and Roshanbin introduced in 2016 the burning number $b(G)$ of any finite graph $G$. They…
The burning number is a recently introduced graph parameter indicating the spreading speed of content in a graph through its edges. While the conjectured upper bound on the necessary numbers of time steps until all vertices are reached is…