If $X$ is a set, we let $[X]^2= \big\{\{a,b\}: a \neq b \in X \big\}$. Given a simple, undirected graph $G=(V,E)$, we let $\delta(G)$ be its minimum degree, and $\Delta(G)$ its maximum degree. W say that $G$ is self-complementary if $G \cong \bar{G}$ where $\bar{G} = (V, [V]^2\setminus E)$.

Given $N\in\mathbb{N}$, is there a self-complimentary graph $G$with $\Delta(G) \geq N\cdot \delta(G)$?