K4, 4 - e has no finite planar cover

نویسنده

Petr Hlineý

چکیده

A graph G has a planar cover if there exists a planar graph H , and a homomorphism φ : H → G that maps the neighbours 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 non-projective graph has a finite planar cover. From the list there remain only two cases not solved yet—the graphs K 4,4 − e and K1,2,2,2. We prove the non-existence of a finite planar cover of K4,4−e.

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