3 problems

Let $G$ be a graph from a class with polynomial $\omega$-expansion, let $q$ be the vertex-cost function, and let $\ell$ be the parameter in the separator theorem. A set $C\cup M$ i…

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…

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