The 5-cycle double cover conjecture for graphic matroids

A graphic matroid is the cycle matroid of a graph. A coloop is an element belonging to every basis, and a $k$-cycle double cover of a matroid is a family of at most $k$ cycles such that every element belongs to exactly two members.

Graphic matroid 5-cycle double cover conjecture. Every graphic matroid without coloops has a $5$-cycle double cover.

This is the matroid formulation of the graph-theoretic $5$-cycle double cover conjecture. The source establishes an eight-cycle bound for graphic matroids without coloops but leaves the five-cycle bound open.