Geelen's chi-boundedness conjecture for graphs excluding a vertex-minor

Let $H$ be a graph. A class of graphs is $\chi$-bounded if there exists a function $f:\mathbb N\rightarrow\mathbb N$ such that for every graph $G$ in the class and every induced subgraph $J$ of $G$, $\chi(J)\leq f(\omega(J))$, where $\chi(J)$ and $\omega(J)$ denote the chromatic and clique numbers of $J$, respectively. A vertex-minor of a graph is an induced subgraph of a graph obtained by a sequence of local complementations. Geelen's conjecture. For every graph $H$, the class of graphs with no $H$ vertex-minor is $\chi$-bounded. This conjecture extends known $\chi$-boundedness results for circle graphs and graphs of bounded rank-width; its general case remains open.