A note on possible extensions of Negami's conjecture
Petr Hliněný · Journal of Graph Theory · 1999
A graph H is a cover of a graph G, if there exists a mapping φ from V(H) onto V(G) such that for every vertex υ of G, φ maps the neighbors of υ in H bijectively onto the neighbors of φ(υ) in G. Negami conjectured in 1987 that a connected graph has a finite planar cover if and only if it embeds in the projective plane. This conjecture is not completely solved yet, but partial results due to Archdeacon, Fellows, Negami, and the author are known. This article suggests another formulation of this conjecture that has a straightforward generalization to higher nonorientable surfaces, and provides some support for the generalized version. © 1999 John Wiley & Sons, Inc. J Graph Theory 32: 234–240 1999