Projective-planar double coverings of graphs (Q1767623)

A connected graph \(\widetilde G\) is a cover of \(G\) if there is a surjection \(\phi :V(\widetilde{G}) \rightarrow V(G)\) such that at each vertex \(\widetilde v\), the incident edges map bijectively to the edges incident to \(\phi(\widetilde{v})\). Negami's planar-cover conjecture states that a graph has a planar cover if and only if it embeds in the projective plane. The author proves here that a connected graph is projective planar if and only if it has a projective-planar double covering. He also shows that any projective-planar double covering of a 2-connected graph is planar.