Regional connectivity and circuit enumeration in planar graphs

The region-adjacency matrix of a planar graph G is the vertex-adjacency matrix of its geometric dual G´. Thus, regional connectivity in G has precisely the properties of vertex connectivity in G´. This duality is used to advantage in a routine presented in the paper for enumerating all the circuits in G from the set of vertex cutsets in G´. The routine yields each circuit uniquely, and circumvents a certain combinatorial tedium which is present in circuit-enumeration techniques proposed previously by Rao et al. and Maxwell and Reed.