Power-of-two cycles in projective cubic graphs of large edge-width

Source abstract

Heckman and Krakovski proved that every 3-connected cubic planar graph contains a cycle of length 2^m for some 2 $\le$ m $\le$ 7. We extend this to 3-connected cubic graphs embedded in the real projective plane with face-width at least three and edge-width at least 48; the cycle may moreover be taken contractible. The argument passes to the spherical double cover, where the planar theorem provides the cycle inside a subgraph of diameter at most 47, and the condition on the edge-width guarantees that this subgraph projects injectively.