All graphs here are finite and simple.

A $d$-factor of a graph is a spanning regular subgraph of degree $d$.

Where can I find theorems of this nature, for constants $a,b,c\gt 0$: If $G$ is a graph with all degrees in $[an,bn]$, and $d$ is an even integer in $[0,cn]$, then $G$ has a $d$-factor?