Szekeres–Seymour cycle double cover conjecture

Let $\operatorname{\mathcal{G}}=(V,E)$ be a bridgeless cubic graph. A cycle double cover of $\operatorname{\mathcal{G}}$ is a set of cycles in which every arc of $\operatorname{\mathcal{G}}$ is contained in exactly two cycles. Cycle double cover conjecture. Every bridgeless cubic graph has a cycle double cover. The conjecture concerns the existence of such covers for all bridgeless cubic graphs; arbitrary cycle double covers are not known to exist in general.