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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(...

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