3-connected reduction for regular graph covers

A regular covering projection G0→H0 induces regular covering projections Gi→Hi where Hi is the ith quotient reduction of H0. This property allows to construct all possible quotients H0 of G0 from the possible quotients Hr of Gr. By applying this method to planar graphs, we give a proof of Negami's Theorem (1988). Our structural results are also used in subsequent papers for regular covering testing when G is a planar graph and for an inductive characterization of the automorphism groups of planar graphs (see Babai (1973) as well).