For a finite, simple, undirected graph $G=(V,E)$ let $\delta(G)$ and $\Delta(G)$ denote the minimum and maximum degree of $G$, respectively.
Is there a constant $K\in\mathbb{N}$ with the following property?
Whenever $n,k$ are integers with $n\geq 4, k\geq 1$ and $n>k$, there is a $k$-vertex critical graph $G=(V,E)$ with $|V|=n$ and $\Delta(G)-\delta(G) \leq K$.