Burning graphs - a probabilistic perspective

TL;DR

This paper explores the probabilistic properties of the burning number in various random graph models and introduces new probabilistic variants of the burning process, providing insights into their behavior.

Contribution

It analyzes the burning number in binomial random graphs, geometric graphs, and Cartesian products, and introduces new probabilistic variants of the burning sequence.

Findings

Analyzed the burning number for G(n,p), geometric graphs, and Cartesian products.

Introduced and studied new probabilistic variants of the burning number.

Provided theoretical insights into the behavior of these parameters.

Abstract

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), random geometric graphs, and the Cartesian product of paths. Moreover, new variants of the burning number are introduced in which a burning sequence of vertices is selected according to some probabilistic rules. We analyze these new graph parameters for paths.