A Note on 5-Cycle Double Covers

The strong cycle double cover conjecture states that for every circuit C of a bridgeless cubic graph G, there is a cycle double cover of G which contains C. We conjecture that there is even a 5-cycle double cover S of G which contains C, i.e. C is a subgraph of one of the five 2-regular subgraphs of S. We prove a necessary and sufficient condition for a 2-regular subgraph to be contained in a 5-cycle double cover of G.