Mader's tree-removability conjecture

For $k\ge 1$ and any tree $T$ of order $m$, let $G$ be a $k$-connected graph with minimum degree $\delta(G)\ge \left\lfloor 3k/2\right\rfloor+m-1$. A subtree $T'$ is isomorphic to $T$ when $T'\cong T$. Mader's tree-removability conjecture. Every such graph $G$ contains a subtree $T'\cong T$ such that $G-V(T')$ is $k$-connected. This extends Mader's path-removability theorem from paths to arbitrary trees. The conjecture is known for paths, for $k=1$, for particular families of trees, for $2$-connected graphs, and for $k\le 3$; it remains open for $k\ge 4$.