Kriesell's spanning-tree deletion conjecture

Let $k$ be a positive integer. A graph is $r$-connected if it remains connected after deletion of fewer than $r$ vertices. For a spanning tree $T$ of a graph $G$, write $G-E(T)$ for the graph obtained by deleting all edges of $T$.

Kriesell's conjecture. There exists a smallest integer $g(k)$ such that every $g(k)$-connected graph $G$ contains a spanning tree $T$ for which

$$G-E(T)\text{ is }k\text{-connected}.$$

The paper's packing theorem implies this conjecture, with an explicit bound obtained from the paper's results. Earlier work established the case $k=2$, while the edge-connected analogue follows from the Nash-Williams–Tutte theorem.