Let $G=(V,E)$ be a finite, simple, undirected graph. The *Hadwiger number* $\eta(G)$ is the maximum $n\in\mathbb{N}$ such that $K_n$ is a minor of $G$.

Hadwiger's celebrated conjecture states that $\chi(G) \leq \eta(G)$ for every finite graph $G$.

A crude approximation "from below" for $\chi(G)$ is $|V(G)|/\alpha(G)$ where $\alpha(G)$ is the size of the largest independent set in $G$. We get $|V(G)|/\alpha(G) \leq \chi(G)$ because every coloring is a partition of $V(G)$ into independent sets.

**Question.** Is $|V(G)|/\alpha(G) \leq \eta(G)$ for all finite graphs $G$?