2 problems

Let $G_{n,p=c/n}$ be the Erdős–Rényi random graph, and let $c_k$ denote the threshold for the appearance of a non-empty $k$-core, meaning a maximal subgraph with minimum degree at…

Let $G\sim\mathbb{G}(n,\lambda/n)$ be a random graph, where $k\geq 3$ and $\lambda>0$ are constants. The $k$-core of $G$, denoted $\mathrm{core}_{k}(G)$, is the largest induced sub…