K4,4 ?e has no finite planar cover
Petr Hlin � · Journal of Graph Theory · 1998
A graph G has a planar cover if there exists a planar graph H, and a homomorphism φ : H → G that maps the neighbors of each vertex bijectively. Each graph that has an embedding in the projective plane also has a finite planar cover. Negami conjectured the converse in 1988. This conjecture holds as long as no minor-minimal nonprojective graph has a finite planar cover. From the list there remain only two cases not solved yet—the graphs K4,4 − e and K1,2,2,2. We prove the nonexistence of a finite planar cover of K4,4 − e. © 1998 John Wiley & Sons, Inc. J Graph Theory 27: 51–60, 1998