The equality conjecture for shortest cycle covers and triangle expansions

Let $G$ be a cubic graph. For $U\subseteq V(G)$, let $G_U$ be the cubic graph obtained by expanding each vertex of $U$ into a triangle. For a bridgeless cubic graph $G$, let $T(G)$ be the minimum size of a set $U$ such that the edge-set of $G_U$ can be covered with four perfect matchings. Let $scc(G)$ denote the length of a shortest cycle cover of $G$. Equality conjecture for $scc(G)$ and $T(G)$. If $G$ is a $3$-edge-connected cubic graph, then

$$scc(G)=\frac{4}{3}|E(G)|+T(G).$$

The paper proves the corresponding inequality for bridgeless cubic graphs and proposes equality under the stronger $3$-edge-connectivity assumption. The conjecture remains open.