  For positive integers $n$ and $e$, let $\kappa(n,e)$ be the minimum crossing
number (the standard planar crossing number) taken over all graphs with $n$
vertices and at least $e$ edges. Pach, Spencer and T\'oth [Discrete and
Computational Geometry 24 623--644, (2000)] showed that $\kappa(n,e) n^2/e^3$
tends to a positive constant (called midrange crossing constant) as $n\to
\infty$ and $n \ll e \ll n^2$, proving a conjecture of Erd\H{o}s and Guy. In
this note, we extend their proof to show that the midrange crossing constant
exists for graph classes that satisfy a certain set of graph properties. As a
corollary, we show that the the midrange crossing constant exists for the
family of bipartite graphs. All these results have their analogues for
rectilinear crossing numbers.
