Suppose $G$ is a finite simple graph and $\eta(G)$ is the maximum $n\in\mathbb{N}$ such that $K\_n$ is a minor of $G$. If $\delta(G)$ is the minimal degree of $G$, do we have $\delta(G)\leq\eta(G)$?



Hadwiger number and minimal degree
No, icosahedron does not have $K\_5$ as a minor being planar graph.


