Alon–Tarsi shortest cycle cover conjecture for bridgeless graphs

Let $G$ be a bridgeless graph, and let a circuit cover be a family of circuits covering every edge of $G$. Its length is the sum of the numbers of edges in its circuits. Alon–Tarsi conjecture. Every bridgeless graph $G$ has a circuit cover with length at most

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

This is the Shortest Cycle Cover Conjecture, concerning the minimum total length of circuit covers of bridgeless graphs. The conjecture is presented as a well-known open problem in the source.