On the parity of planar covers
Dan Archdeacon, R. Bruce Richter · Journal of Graph Theory · 1990
Abstract A covering is a graph map ϕ: G → H that is an isomorphism when restricted to the star of any vertex of G. If H is connected then |ϕ−1(v)| is constant. This constant is called the fold number. In this paper we prove that if G is a planar graph that covers a nonplanar H, then the fold number must be even.