We study the cover time of a random graph chosen uniformly at random from the set of graphs with vertex set $[n]$ and degree sequence $\mathbf{ d}=(d_i)_{ i=1}^n$. In a previous work, the asymptotic cover time was obtained under a number of assumptions on $\mathbf{ d}$, the most significant being that $d_i\geq 3$ for all $i$. Here we replace this assumption by $d_i\geq 2$. As a corollary, we establish the asymptotic cover time for the 2-core of the emerging giant component of $\mathcal{ G}(n,p)$.
Categories: math.CO math.PR