发表机构
University of Science and Technology of China（中国科学技术大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明图副本的均匀测度具有特定spread性质，从而给出分数期望阈值上界，并针对树和最大度受限图移除对数因子，验证了第二Kahn-Kalai猜想。
AI 中文摘要
我们证明，图$H$的副本上的均匀测度是$Cq_H\log(2e(H))$-spread的，其中$q_H$是其图形期望阈值，定义为期望计数为1。这给出了至多$C\pe(H)\log(2e(H))$的分数期望阈值。对于树以及最大度至多为其平均度的指数函数的图，我们移除了对数损失。因此，“第二”Kahn-Kalai猜想对所有此类图成立。
英文摘要
We show that the uniform probability measure on copies of a nonempty graph $H$ in $K_n$ is $Cq_H\log(2e(H))$-spread, where $q_H$ is its graphic expectation threshold. Consequently, the fractional expectation threshold of $H$ is at most $Cq_H\log(2e(H))$. We remove the logarithmic factor for trees and for graphs whose average degree is at least the logarithm of their maximum degree. This proves the ``second'' Kahn-Kalai conjecture for these two classes, which encompass most of the standard families studied in random graph containment problems.
Comments17 pages
