The cycle double cover conjecture says that for every undirected bridgeless graph there is a list of cycles such that every edge of the graph belongs to exactly two of the cycles. It is well known that the cycle double cover conjecture is true if and only if it is true for cubic graphs which are not 3-edge-colourable. Let $G$ be a cubic graph. The author defines a non-trivial 3-edge cut in $G$ to be a 3-edge cut $S$ such that $G-S$ has no trivial components. It is shown in the paper that the cycle double cover conjecture is true if and only if it holds for cubic graphs without non-trivial 3-edge cuts.
Reviewer: Zbigniew Lonc (Warszawa)