Semi-duality and the cycle double cover conjecture
In what follows, all matroids are binary. A cycle is a disjoint union of circuits. Two matroids are called semi-dual if every cocycle of one of them is a cycle of the other. A cycle double cover (CDC) of a matroid is a family of not necessarily distinct cycles, containing every element of the underlying set exactly twice. The CDC-conjecture (that every bridgeless graph has a CDC) is shown to be equivalent to the statement: Every bridgeless regular matroid has a loopless graphic semi-dual. As an application, the author shows that every bridgeless multigraph containing a Hamiltonian path has a CDC consisting of at most 6 Eulerian subgraphs.
scientific article; zbMATH DE number 3981186