Regular Graph Covering

3-connected Reduction for Regular Graph Covers

We describe reductions which produce a series of graphs such that is created from by replacing certain inclusionminimal subgraphs with colored edges.The process ends with a primitive graph which is either 3-connected, or a cycle.This reduction can be viewed as a non-trivial modification of reductions of mac lane (1937), trachtenbrot (1958), tutte (1966), hopcroft and tarjan (1973), cuningham andedmonds (1980), walsh (1982), and others.Our structural results are also used in subsequent papers for regular covering testing when is a planar graph and for an inductive characterization of the automorphism groups of planar graphs.