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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

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

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

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

Motivated by the burning and cooling processes, the burning game is introduced. The game is played on a graph $G$ by the two players (Burner and Staller) that take turns selecting vertices of $G$ to burn; as in the burning process, burning…

Combinatorics · Mathematics 2024-09-18 Nina Chiarelli , Vesna Iršič , Marko Jakovac , William B. Kinnersley , Mirjana Mikalački

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 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

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

We introduce a new graph parameter called the cooling number, inspired by the spread of influence in networks and its predecessor, the burning number. The cooling number measures the speed of a slow-moving contagion in a graph; the lower…

Combinatorics · Mathematics 2024-01-09 Anthony Bonato , Trent G. Marbach , Holden Milne , Teddy Mishura

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 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

Graph burning is a discrete-time process that models the spread of influence in a network. Vertices are either burning or unburned, and in each round, a burning vertex causes all of its neighbours to become burning before a new fire source…

Combinatorics · Mathematics 2024-09-24 Karen Gunderson , William Kellough , JD Nir , Hritik Punj

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 spread of an infection, a contagion, meme, emotion, message and various other spreadable objects have been discussed in several works. Burning and firefighting have been discussed in particular on static graphs. Graph burning simulates…

Physics and Society · Physics 2023-11-17 Arya Tanmay Gupta

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 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…

Combinatorics · Mathematics 2024-09-04 Ta Sheng Tan , Wen Chean Teh

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

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

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

The burning number $b(G)$ of a graph $G$ is the minimum number of rounds required to burn all vertices when, at each discrete step, existing fires spread to neighboring vertices and one new fire may be ignited at an unburned vertex. This…

Combinatorics · Mathematics 2026-03-03 John Peca-Medlin
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