论文标题
燃烧的数字猜想渐近地持有
The Burning Number Conjecture Holds Asymptotically
论文作者
论文摘要
图$ g $的燃烧数字$ b（g）$是燃烧图形所有顶点所需的最小圈，如果启动新的火灾，现有的火灾蔓延到所有相邻的顶点。 Bonato等人的燃烧数字猜想。 （2016）假设$ b（g）\ leq \ left \ lceil \ sqrt {n} \ right \ rceil $ for $ n $ vertices上的所有图形$ g $。我们证明了这个猜想是渐近地持有的，即$ b（g）\ leq（1+o（1））\ sqrt n $。
The burning number $b(G)$ of a graph $G$ is the smallest number of turns required to burn all vertices of a graph if at every turn a new fire is started and existing fires spread to all adjacent vertices. The Burning Number Conjecture of Bonato et al. (2016) postulates that $b(G)\leq \left\lceil\sqrt{n}\right\rceil$ for all graphs $G$ on $n$ vertices. We prove that this conjecture holds asymptotically, that is $b(G)\leq (1+o(1))\sqrt n$.
