地核是如何位于地幔内部的？
How does the core sit inside the mantle?
摘要：
随机图$G(n,p)$的最小度$k$的最大子图定义为$k$ -核，它已被广泛研究.在一篇具有里程碑意义的论文中，Pittel、Wormald和Spencer [JCTB 67（1996）111- 151]确定了出现大面积$k$核的阈值$d_k$。在这里，我们推导出一个多类型的高尔顿-沃森分支过程，精确地描述了如何$k$核心嵌入到随机图的任何$k\geq3$和任何固定的平均度$d=np>d_k$。这概括了先前的结果，例如，$k$内核的内部结构。
英文摘要：
The $k$-core, defined as the largest subgraph of minimum degree $k$, of the random graph $G(n,p)$ has been studied extensively. In a landmark paper Pittel, Wormald and Spencer [JCTB 67 (1996) 111--151] determined the threshold $d_k$ for the appearance of an extensive $k$-core. Here we derive a multi-type Galton-Watson branching process that describes precisely how the $k$-core is embedded into the random graph for any $k\geq3$ and any fixed average degree $d=np>d_k$. This generalises prior results on, e.g., the internal structure of the $k$-core.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
