Georgia Institute of Technology College of Sciences

Graph burning is a simplified model for the spread of influence in a network. Associated with the process is the burning number, which quantifies the speed at which the influence spreads to every vertex. The Burning Number Conjecture claims that for every connected graph $G$ of order $n,$ its burning number satisfies $b(G) \le \lceil \sqrt{n} \rceil$. While the conjecture remains open, we prove the best-known bound on the burning number of a connected graph $G$ of order $n,$ given by $b(G) \le \sqrt{4n/3} + 1$, improving on the previously known $\sqrt{3n/2}+O(1)$ bound.