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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 extend the notion of chip-firing to weighted graphs, and generalize the Greedy Algorithm and Dhar's Burning Algorithm to weighted graphs. For a vertex $q \in V(\Gamma)$, we give an upper bound for the number of linearly equivalent…

Combinatorics · Mathematics 2023-11-02 Ben Doyle

Given a graph $G=(V,E)$, the problem of \gb{} is to find a sequence of nodes from $V$, called burning sequence, in order to burn the whole graph. This is a discrete-step process, in each step an unburned vertex is selected as an agent to…

Data Structures and Algorithms · Computer Science 2022-09-16 Rahul Kumar Gautam , Anjeneya Swami Kare , Durga Bhavani S

The problem of identifying important players in a given network is of pivotal importance for viral marketing, public health management, network security and various other fields of social network analysis. In this work we find the most…

Discrete Mathematics · Computer Science 2017-11-03 Juvaria Tariq , Muhammad Ahmad , Imdadullah Khan , Mudassir Shabbir

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

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 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…

Data Structures and Algorithms · Computer Science 2020-08-21 Rahul Kumar Gautam , Anjeneya Swami Kare , S. Durga Bhavani

Two kinds of approximation algorithms exist for the k-BALANCED PARTITIONING problem: those that are fast but compute unsatisfying approximation ratios, and those that guarantee high quality ratios but are slow. In this paper we prove that…

Computational Complexity · Computer Science 2019-04-29 Andreas Emil Feldmann

One of the most elementary spreading models on graphs can be described by a fire spreading from a burning vertex in discrete time steps. At each step, all neighbors of burning vertices catch fire. A well-studied extension to model fire…

Data Structures and Algorithms · Computer Science 2025-12-22 Jannis Blauth , Christian Nöbel , Rico Zenklusen

This study explores the vaccine prioritization strategy to reduce the overall burden of the pandemic when the supply is limited. Existing methods conduct macro-level or simplified micro-level vaccine distribution by assuming the homogeneous…

Populations and Evolution · Quantitative Biology 2023-05-10 Lu Ling , Washim Uddin Mondal , Satish V , Ukkusuri

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 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…

Combinatorics · Mathematics 2021-11-03 Mohamed Omar , Vibha Rohilla

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

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

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 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

We introduce a graph partitioning problem motivated by computational topology and propose two algorithms that produce approximate solutions. Specifically, given a weighted, undirected graph $G$ and a positive integer $k$, we desire to find…

Combinatorics · Mathematics 2019-07-04 Abdel-Rahman Madkour , Phillip Nadolny , Matthew Wright

We propose a network protocol similar to the $k$-tree protocol of Itai and Rodeh [{\em Inform.\ and Comput.}\ {\bf 79} (1988), 43--59]. To do this, we define an {\em $t$-uncovering-by-bases} for a connected graph $G$ to be a collection…

Combinatorics · Mathematics 2011-04-14 Robert F. Bailey , Brett Stevens

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…

Data Structures and Algorithms · Computer Science 2023-07-18 Rahul Kumar Gautam , Anjeneya Swami Kare , S. Durga Bhavani

The outbreak of a pandemic, such as COVID-19, causes major health crises worldwide. Typical measures to contain the rapid spread usually include effective vaccination and strict interventions (Nature Human Behaviour, 2021). Motivated by…

Social and Information Networks · Computer Science 2025-03-31 Gargi Bakshi , Sujoy Bhore , Suraj Shetiya