  The Hadwiger number $h(G)$ is the order of the largest complete minor in $G$.
Does sufficient Hadwiger number imply a minor with additional properties?
  In [2], Geelen et al showed $h(G)\geq (1+o(1))ct\sqrt{\ln t}$ implies $G$ has
a bipartite subgraph with Hadwiger number at least $t$, for some explicit
$c\sim 1.276\dotsc$. We improve this to $h(G) \geq (1+o(1))t\sqrt{\log_2 t}$,
and provide a construction showing this is tight. We also derive improved
bounds for the topological minor variant of this problem.
