A survey of graph burning

TL;DR

This survey reviews the current state of research on graph burning, a process modeling influence spread in graphs, highlighting key results, conjectures, and open problems related to the burning number.

Contribution

It provides a comprehensive overview of bounds, conjectures, and algorithms for the burning number, including recent advances and open challenges.

Findings

Summary of state-of-the-art results on the burning number conjecture

Analysis of burning numbers across different graph classes

Discussion of algorithmic complexity and open problems

Abstract

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 survey results on graph burning, focusing on bounds, conjectures, and algorithms related to the burning number. We will discuss state-of-the-art results on the burning number conjecture, burning numbers of graph classes, and algorithmic complexity. We include a list of conjectures, variants, and open problems on graph burning.