Semi-duality and the cycle double cover conjecture

AbstractDefine two binary matroids on the same element set to be mutually semi-dual if every cocycle of one of them is a cycle of the other. We observe that the cycle double cover (CDC) conjecture is equivalent to the following statement: Every bridgeless regular matroid has a loopless graphic semi-dual. This observation is used to construct CDCs for some families of graphs. The main result: Every bridgeless multigraph which contains a Hamiltonian path has a CDC consisting of at most 6 Eulerian subgraphs