Planar presentation characterization conjecture

A planar presentation is a group presentation satisfying the paper's planar condition, namely admitting a suitable assignment of spin flags so that relations do not cross. Planar presentation characterization conjecture. Every planar Cayley graph has a planar presentation, and conversely every planar presentation gives rise to a planar Cayley graph. The supplied text does not state a resolution of this characterization beyond the cubic results proved in the paper.