Kanté–Kwon conjecture on vertex-minors of forests in graphs of large linear rank-width

Let $T$ be a fixed forest, and let $f(T)$ denote an integer depending on $T$. A graph has linear rank-width at least $f(T)$ when its linear rank-width is at least that integer.

Kanté–Kwon conjecture. For every fixed forest $T$, there is an integer $f(T)$ such that every graph of linear rank-width at least $f(T)$ contains a vertex-minor isomorphic to $T$.

This conjecture is an analogue for linear rank-width of Oum's conjecture for rank-width. The source presents it as an open problem, and no resolution is given here.