TITLE: Existence of regular factors in dense graphs
QUESTION [5 upvotes]: 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?

REPLY [4 votes]: To give at least a possible answer, and for those interested in doing a comprehensive literature search for an actual answer, it seems that the somewhat related survey
http://web.mat.bham.ac.uk/D.Kuehn/bcc09dkdo3.pdf
might be a helpful starting point.