Five-line Fano-flow conjecture

Let $G$ be a bridgeless cubic graph. A 5-line Fano-flow is a Fano-flow in which at most five lines of the Fano plane occur as flow values at vertices. Five-line Fano-flow conjecture. Every bridgeless cubic graph has a 5-line Fano-flow. This is a relaxation of the four-line Fano-flow conjecture and is equivalent to the corresponding formulation using two 1-factors and a join.