Oum's rank-width conjecture for bipartite circle graphs

A bipartite circle graph is a circle graph whose vertices can be divided into two parts such that edges join only vertices in different parts. A graph $H$ is a pivot-minor of $G$ if it can be obtained from $G$ by pivotings and vertex deletions, and the rank-width of $G$ is its graph rank-width. Oum's rank-width conjecture. For every bipartite circle graph $H$, every graph $G$ of sufficiently large rank-width contains a pivot-minor isomorphic to $H$. This conjecture proposes a universal obstruction principle linking large rank-width to prescribed bipartite circle-graph pivot-minors; its general status is not resolved in the source.