Hypergraph Hadwiger conjecture for the chromatic number

For an integer $t\geq 2$, let $h(t)$ be the largest chromatic number of a hypergraph with no $K_t$-minor; the paper establishes that this quantity exists. A hypergraph is $K_t$-minor-free if it does not contain $K_t$ as a minor, where hypergraph minors are obtained by deleting vertices or hyperedges and contracting hyperedges. Hypergraph Hadwiger conjecture. For every integer $t\geq 2$,

$$h(t)=\left\lceil\frac{3}{2}(t-1)\right\rceil.$$

Equivalently, every $K_t$-minor-free hypergraph $H$ satisfies

$$\chi(H)\leq\left\lceil\frac{3}{2}(t-1)\right\rceil.$$

The lower bound is attained by complete $3$-uniform hypergraphs, so the conjecture would give the exact extremal chromatic number. The conjecture remains open even for $K_3$-minor-free hypergraphs.