2 problems

Polynomial weak colouring-number conjecture. There exists a function $f$ such that for every $K^*_{s,t}$-minor-free graph $G$ and every $r\geqslant1$,

Bounded-path partition conjecture. For all $t\geqslant s\geqslant1$, there exists an integer $p$ such that every $K^*_{s,t}$-minor-free graph $G$ has a connected partition…