Atlantic Graph Theory Seminar

Title: Graph burning, the burning number conjecture, and burning density

Abstract: Graph burning is a discrete time process on a graph that acts as a simple model for the spread of social contagion in a network. Graph burning was introduced by Bonato, Janssen and Roshanbin in 2014, and with this introduction came the now famous “burning number conjecture”. In the first half of my talk, I will introduce graph burning and give a brief overview of the progress made towards the burning number conjecture. Then, for the remainder of the talk, I will introduce a variation of graph burning in which the graph grows over time. In this variation, if the graph grows fast enough then we may never be able to burn all of the vertices at any given time. We are instead interested in the “burning density”, i.e., the limiting ratio of burning vertices to all vertices. The talk will conclude with some new results by Gunderson, Nir, Pralat, and myself, classifying the obtainable burning densities on growing grid-graphs.