  Let $G$ be a $d$-regular graph on $n$ vertices. Frieze, Gould, Karo\'nski and
Pfender began the study of the following random spanning subgraph model
$H=H(G)$. Assign independently to each vertex $v$ of $G$ a uniform random
number $x(v) \in [0,1]$, and an edge $(u,v)$ of $G$ is an edge of $H$ if and
only if $x(u)+x(v) \geq 1$. Addressing a problem of Alon and Wei, we prove that
if $d = o(n/(\log n)^{12})$, then with high probability, for each nonnegative
integer $k \leq d$, there are $(1+o(1))n/(d+1)$ vertices of degree $k$ in $H$.
