Pivot-minor chi-boundedness conjecture

For a graph $H$, a graph class has no pivot-minor isomorphic to $H$ if none of its members has such a pivot-minor. Pivot-minor conjecture. For every graph $H$, the class of graphs having no pivot-minor isomorphic to $H$ is $\chi$-bounded. This would imply Geelen's vertex-minor conjecture because every pivot-minor is a vertex-minor; it is proved for several families, including pivot-minors of cycles and suitable trees, but remains open in general.