The redundant-tree conjecture for highly connected graphs

Let $T$ be a tree of order $m$, and let $G$ be a $k$-connected graph. Write $\delta(G)$ for the minimum degree of $G$. A tree subgraph is $k$-redundant if it has the redundancy property intended in the source. Redundant-tree conjecture. If

$$\delta(G)\geq\left\lfloor\frac{3k}{2}\right\rfloor+m-1,$$

then $G$ contains a $k$-redundant tree isomorphic to $T$. This conjecture proposes a degree condition ensuring a prescribed redundant tree in a highly connected graph; the supplied text gives no resolution.