The 1/10 upper-bound conjecture for triangle expansions

Let $G$ be a bridgeless cubic graph. For $U\subseteq V(G)$, let $G_U$ be obtained by expanding each vertex of $U$ into a triangle, and let $T(G)$ be the minimum size of a set $U$ for which the edge-set of $G_U$ can be covered with four perfect matchings. The $1/10$ upper-bound conjecture. Every bridgeless cubic graph $G$ satisfies

$$T(G)\leq \frac{|V(G)|}{10}.$$

The paper proves the weaker bound $T(G)\leq \frac{2}{5}|V(G)|$ assuming the 5-cycle double cover conjecture. The proposed bound remains open.