Alon–Tarsi–Jaeger short cycle cover conjecture

Let $G$ be a bridgeless graph with $m$ edges. A cycle cover of $G$ is a multiset of cycles from $G$ such that every edge of $G$ belongs to at least one cycle, and its length is the sum of the lengths of its cycles.

Short cycle cover conjecture. Every bridgeless graph with $m$ edges has a cycle cover of length at most $1.4m$.

This conjecture was independently proposed by Alon and Tarsi and by Jaeger. The paper proves weaker bounds for bridgeless cubic graphs, so the stated $1.4m$ bound remains unresolved here.