标题： 中等稀疏随机图中诱导子树最大尺寸的集中性 显示英文标题

标题： Concentration of the maximum size of an induced subtree in moderately sparse random graphs

摘要： Kamaldinov、Skorkin 和 Zhukovskii 证明了，当$p\in(0,1)$是一个常数时，二项式随机图$G(n,p)$中的诱导子树的最大大小集中在两个连续点上。 利用对诱导子树数量的二阶矩的改进界限，我们表明当$n^{-\frac{e-2}{3e-2}+\varepsilon}\leq p=o(1)$时，同样的结果仍然成立。 显示英文摘要

摘要： Kamaldinov, Skorkin, and Zhukovskii proved that the maximum size of an induced subtree in the binomial random graph $G(n,p)$ is concentrated at two consecutive points, whenever $p\in(0,1)$ is a constant. Using improved bounds on the second moment of the number of induced subtrees, we show that the same result holds when $n^{-\frac{e-2}{3e-2}+\varepsilon}\leq p=o(1)$.