论文标题
弱饱和稳定性的阈值
Threshold for weak saturation stability
论文作者
论文摘要
我们研究了Erdős-rényi随机图的弱$ k_s $ - 饱和数$ \ mathbbmsl {g}（n，p）$，由$ \ mathrm {wsat}（\ mathbbmsl {g Mathbmsl {g}（n，p），k_s，k_s）$，$ k_s $ s $ shuptice。 Korándi和Sudakov在2017年证明，$ k_s $ - 饱和$ k_n $的饱和数是稳定的，从某种意义上说，它在以持续的概率上删除边缘后保持不变。在本文中，我们证明存在该稳定性属性的阈值，并在阈值上给出上和下限。这概括了Korándi和Sudakov的结果。还提供了$ \ mathrm {wsat}（\ mathbbmsl {g}（n，p），k_s）$的一般上限。
We study the weak $K_s$-saturation number of the Erdős--Rényi random graph $\mathbbmsl{G}(n, p)$, denoted by $\mathrm{wsat}(\mathbbmsl{G}(n, p), K_s)$, where $K_s$ is the complete graph on $s$ vertices. Korándi and Sudakov in 2017 proved that the weak $K_s$-saturation number of $K_n$ is stable, in the sense that it remains the same after removing edges with constant probability. In this paper, we prove that there exists a threshold for this stability property and give upper and lower bounds on the threshold. This generalizes the result of Korándi and Sudakov. A general upper bound for $\mathrm{wsat}(\mathbbmsl{G}(n, p), K_s)$ is also provided.
