Minimum degree $k$ and $k$-connectedness usually arrive together
Minimum degree $k$ and $k$-connectedness usually arrive together
Let $d,n\in \mathbb{N}$ be such that $d=\omega(1)$, and $d\le n^{1-a}$ for some constant $a>0$. Consider a $d$-regular graph $G=(V, E)$ and the random graph process that starts with the empty graph $G(0)$ and at each step $G(i)$ is obtained from $G(i-1)$ by adding uniformly at random a new edge from …