The $3/2$-List Hadwiger conjecture

Let $t\in\mathbb{N}$ and let $G$ be a graph. A $K_t$-minor-free graph is a graph that does not contain a $K_t$-minor, and $\chi_\ell(G)$ denotes its list chromatic number. The $3/2$-List Hadwiger conjecture. Every $K_t$-minor-free graph $G$ satisfies

$$\chi_\ell(G)\le \frac{3}{2}t.$$

This is the stronger quantitative form of the List Hadwiger conjecture proposed by Kawarabayashi and Mohar and recorded in Seymour's survey. It is open; the paper disproves the earlier stronger possibility with coefficient $1$ and proves that any valid coefficient must be at least $2-o(1)$ asymptotically.