Alon's partition conjecture for inversion number

For an oriented graph $D$ and a vertex subset $V_i$, write $D\langle V_i\rangle$ for the subdigraph induced by $V_i$; let $\operatorname{inv}(D)$ denote inversion number.

Alon's inversion-number partition conjecture. For every two positive integers $k_1,k_2$, there exists an integer $f(k_1,k_2)$ such that every oriented graph $D$ with

$$\operatorname{inv}(D)\geq f(k_1,k_2)$$

admits a partition $(V_1,V_2)$ of $V(D)$ satisfying

$$\operatorname{inv}(D\langle V_i\rangle)\geq k_i\quad\text{for }i=1,2.$$

This asks for an inversion-number analogue of Alon's minimum-out-degree partition conjecture: sufficiently large global inversion number should force both parts to retain prescribed inversion complexity. The source does not state a resolution.