We prove that $G_{n,p=c/n}$ w.h.p. has a k-regular subgraph if c is at least $e^{-\mathrm{\Theta }(k)}$ above the threshold for the appearance of a subgraph with minimum degree at least k; i.e. a non-empty k-core. In particular, this pins down the threshold for the appearance of a k-regular subgraph to a window of size $e^{-\mathrm{\Theta }(k)}$.

中文翻译：

---

靠近随机图k核心阈值的k正则子图

我们证明 $G_{ñ，p=C/ñ}$如果c至少为w，则whp具有k个正则子图${Ë}^{-\mathrm{\Theta }（ķ）}$高于最小度至少为k的子图出现的阈值; 即非空的k核。特别是，这将k正则子图的出现阈值固定为一个${Ë}^{-\mathrm{\Theta }（ķ）}$。