Kawarabayashi–Ozeki conjecture on disjoint paths preserving connectivity

Let $k$ and $l$ be positive integers. A graph is $r$-connected if deleting fewer than $r$ vertices leaves it connected. For a graph $G$ and paths $P_1,\ldots,P_k$, write $G-\bigcup_{i=1}^k V(P_i)$ for the graph obtained by deleting all vertices on those paths.

Kawarabayashi–Ozeki conjecture. There exists a function $f(k,l)$ such that, for every $f(k,l)$-connected graph $G$ and two distinct vertices $s$ and $t$ in $G$, there are $k$ internally disjoint paths $P_1,\ldots,P_k$ with endpoints $s$ and $t$ such that

$$G-\bigcup_{i=1}^k V(P_i)$$

is $l$-connected.

This conjecture strengthens the cited result that, after deleting one induced path between two specified vertices from a sufficiently highly connected graph, the remainder can be required to be $k$-connected. It asks whether a bounded connectivity assumption likewise permits deleting several internally disjoint $s$–$t$ paths while retaining prescribed connectivity.