# Minimal degree difference for $k$-critical graphs on $n$ vertices

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 $$\Delta(G)-\delta(G) \leq K$$.

• k-[vertex critical] ? Dec 15 '19 at 0:53
• Right - forgot to insert link, will do. Dec 15 '19 at 7:52