Alon and Tarsi's shortest circuit cover conjecture

Let $G$ be a 2-edge-connected cubic graph. A shortest circuit cover of $G$ is a circuit cover having minimum total length, denoted by $\operatorname{scc}(G)$. Alon and Tarsi's conjecture. Every 2-edge-connected cubic graph has a shortest circuit cover with length at most

$$\frac{7|E(G)|}{5}.$$

The conjecture improves the general $5|E(G)|/3$ bound for 2-edge-connected graphs and would give a sharp universal bound for cubic graphs. It is also known as the Shortest Circuit Cover Conjecture and, as noted in the source, implies the Circuit Double Cover Conjecture.