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# Atlantic Graph Theory Seminar: Jérémie Turcotte, Université de Montréal

## February 15, 2023 @ 3:30 pm - 4:30 pm

## Progress towards the Burning Number Conjecture

The burning number *b(G)* of a graph *G* is the smallest integer *k* such that *G* can be covered by *k* balls of radii respectively *0,…,k-1*, and was introduced independently by Brandenburg and Scott at Intel as a transmission problem on processors and Bonato, Janssen and Roshanbin as a model for the spread of information in social networks. The Burning Number Conjecture claims that *b(G)<=\lceil\sqrt{n}\rceil*, where* n* is the number of vertices of *G*. This bound is tight for paths. The previous best bound for this problem, by Bastide et al., was *b(G)<= \sqrt{\frac{4n}{3}}+1*. We prove that the Burning Number Conjecture holds asymptotically, that is *b(G)<= (1+o(1))\sqrt{n}*. Following a brief introduction to graph burning, this talk will focus on the general ideas behind the proof.