Related papers: APX-Hardness and Approximation for the k-Burning N…
Graph burning is a discrete time process which can be used to model the spread of social contagion. One is initially given a graph of unburned vertices. At each round (time step), one vertex is burned; unburned vertices with at least one…
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…
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…
Graph burning is a graph process that models the spread of social contagion. Initially, all the vertices of a graph $G$ are unburnt. At each step, an unburnt vertex is put on fire and the fire from burnt vertices of the previous step…
Motivated by the $k$-center problem in location analysis, we consider the \emph{polygon burning} (PB) problem: Given a polygonal domain $P$ with $h$ holes and $n$ vertices, find a set $S$ of $k$ vertices of $P$ that minimizes the maximum…
Suppose we have a network that is represented by a graph $G$. Potentially a fire (or other type of contagion) might erupt at some vertex of $G$. We are able to respond to this outbreak by establishing a firebreak at $k$ other vertices of…
Graph burning is a natural discrete graph algorithm inspired by the spread of social contagion. Despite its simplicity, some open problems remain steadfastly unsolved, notably the burning number conjecture, which says that every connected…
In 2016, Bonato, Janssen, and Roshanbin introduced graph burning as a discrete process that models the spread of social contagion. Although the burning process is a simple algorithm, the problem of determining the least number of rounds…
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…
We study the problem of covering the maximum number of vertices in a graph by a collection of vertex-disjoint stars, each with a number of satellites in a given interval $[k, \ell]$, where $1 \le k < \ell$ and $\ell$ can be infinity. This…
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 $u_i$.…
A $k$-coloring of a graph is an assignment of integers between $1$ and $k$ to vertices in the graph such that the endpoints of each edge receive different numbers. We study a local variation of the coloring problem, which imposes further…
Given a set $P$ of points in the plane, a point burning process is a discrete time process to burn all the points of $P$ where fires must be initiated at the given points. Specifically, the point burning process starts with a single burnt…
In a graph $G$, a fire starts at some vertex. At every time step, firefighters can protect up to $k$ vertices, and then the fire spreads to all unprotected neighbours. The $k$-surviving rate $\rho_k(G)$ of $G$ is the expectation of the…
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…
In this paper, we introduce the problem of finding an orientation of a given undirected graph that maximizes the burning number of the resulting directed graph. We show that the problem is polynomial-time solvable on K\H{o}nig-Egerv\'{a}ry…
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 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…
The Burning Number Conjecture, that a graph on $n$ vertices can be burned in at most $\lceil \sqrt{n} \ \rceil$ rounds, has been of central interest for the past several years. Much of the literature toward its resolution focuses on two…
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…