West–Wu's conjecture on packing T-connectors

Let $G$ be a graph and $T\subseteq V(G)$ a set of terminals. A $T$-connector is the union of a family of edge-disjoint $T$-paths such that, after shortcutting the paths one by one, the resulting graph has connected induced subgraph on $T$. The set $T$ is $r$-edge-connected in $G$ if no edge-cut of size smaller than $r$ separates two vertices of $T$.

West–Wu's conjecture. For every positive integer $k$, if $T$ is $3k$-edge-connected in $G$, then $G$ admits $k$ pairwise edge-disjoint $T$-connectors.

West and Wu introduced $T$-connectors as a strengthening of Steiner trees. Their conjecture is refuted: the paper constructs infinitely many counterexamples for $k=1$ and for every even $k$. DeVos, McDonald and Pivotto proved the conclusion under the stronger hypothesis that $T$ is $(6k+6)$-edge-connected in $G$.