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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…

Combinatorics · Mathematics 2015-07-24 Anthony Bonato , Jeannette Janssen , Elham Roshanbin

Graph burning is a model for the spread of social contagion. The burning number is a graph parameter associated with graph burning that measures the speed of the spread of contagion in a graph; the lower the burning number, the faster the…

Combinatorics · Mathematics 2015-11-24 Anthony Bonato , Jeannette Janssen , Elham Roshanbin

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…

Combinatorics · Mathematics 2020-09-23 Anthony Bonato

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…

Graph burning studies how fast a contagion, modeled as a set of fires, spreads in a graph. The burning process takes place in synchronous, discrete rounds. In each round, a fire breaks out at a vertex, and the fire spreads to all vertices…

Combinatorics · Mathematics 2019-11-05 Anthony Bonato , Sean English , Bill Kay , Daniel Moghbel

Numerous approaches study the vulnerability of networks against social contagion. Graph burning studies how fast a contagion, modeled as a set of fires, spreads in a graph. The burning process takes place in synchronous, discrete rounds. In…

Combinatorics · Mathematics 2019-04-08 Anthony Bonato , Shahin Kamali

Graph burning is one model for the spread of memes and contagion in social networks. The corresponding graph parameter is the burning number of a graph $G$, written $b(G)$, which measures the speed of the social contagion. While it is…

Combinatorics · Mathematics 2017-08-01 Anthony Bonato , Thomas Lidbetter

Graph burning is a discrete-time process that models the spread of social contagion. Initially, all vertices are unburned. In each round, one unburned vertex is selected and burned, while any unburned vertex that has a burned neighbour from…

Combinatorics · Mathematics 2026-05-01 Jesper Jansson , Shashanka Kulamarva , Yukihiro Murakami , Nikolaas Verhulst

Graph burning is a discrete-time process that models the propagation of information in a network. Initially, we have an undirected graph of unburned vertices. At each time step, an unburned vertex is chosen to burn; additionally, unburned…

Combinatorics · Mathematics 2026-03-17 Dhanyamol Antony , L. Sunil Chandran , Anita Das , Shirish Gosavi , Dalu Jacob , Shashanka Kulamarva

The concept of graph burning and burning number ($bn(G)$) of a graph G was introduced recently [1]. Graph burning models the spread of contagion (fire) in a graph in discrete time steps. $bn(G)$ is the minimum time needed to burn a graph…

Discrete Mathematics · Computer Science 2020-03-23 Zahra Rezai Farokh , Maryam Tahmasbi , Zahra Haj Rajab Ali Tehrani , Yousof Buali

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…

Combinatorics · Mathematics 2023-12-25 Yukihiro Murakami

Our understanding of the dynamics of complex networked systems has increased significantly in the last two decades. However, most of our knowledge is built upon assuming pairwise relations among the system's components. This is often an…

Physics and Society · Physics 2020-04-15 Guilherme Ferraz de Arruda , Giovanni Petri , Yamir Moreno

Graph burning is a discrete process that models the spread of influence through a network using a fire as a proxy for the type of influence being spread. This process was recently extended to hypergraphs. We introduce a variant of…

Combinatorics · Mathematics 2024-08-13 Andrea C. Burgess , John A. Hawkin , Alexander J. M. Howse , Caleb W. Jones , David A. Pike

Graph burning is a round-based game or process that discretely models the spread of influence throughout a network. We introduce a generalization of graph burning which applies to hypergraphs, as well as a variant called ''lazy'' hypergraph…

Combinatorics · Mathematics 2025-08-12 Andrea C. Burgess , Caleb W. Jones , David A. Pike

Graph burning is a simple model for the spread of social influence in networks. The objective is to measure how quickly a fire (e.g., a piece of fake news) can be spread in a network. The burning process takes place in discrete rounds. In…

Combinatorics · Mathematics 2019-09-05 Shahin Kamali , Avery Miller , Kenny Zhang

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…

Combinatorics · Mathematics 2024-11-14 C. B. Jacobs , M. E. Messinger , A. N. Trenk

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…

Combinatorics · Mathematics 2019-10-11 Ta Sheng Tan , Wen Chean Teh

Graph burning runs on discrete time steps. The aim is to burn all the vertices in a given graph in the least number of time steps. This number is known to be the burning number of the graph. The spread of social influence, an alarm, or a…

Data Structures and Algorithms · Computer Science 2021-02-02 Arya Tanmay Gupta , Swapnil A. Lokhande , Kaushik Mondal

In this paper, we study a graph parameter that was recently introduced, the burning number, focusing on a few probabilistic aspects of the problem. The original burning number is revisited and analyzed for binomial random graphs G(n,p),…

Combinatorics · Mathematics 2015-05-13 Dieter Mitsche , Pawel Pralat , Elham Roshanbin

The burning and forcing processes are both instances of propagation processes on graphs that are commonly used to model real-world spreading phenomena. The contribution of this paper is two-fold. We first establish a connection between…

Combinatorics · Mathematics 2026-02-16 Aida Abiad , Pax Mallee
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