Because "G" is triangular, the degree of each vertex in a configuration is known, and all edges internal to the configuration are known, the number of vertices in "G" adjacent to a given configuration is fixed, and they are joined in a cycle. These vertices form the "ring" of the configuration; a configuration with "k" vertices in its ring is a "k"-ring configuration, and the configuration together with its ring is called the "ringed configuration". As in the simple cases above, one may enumerate all distinct four-colorings of the ring; any coloring that can be extended without modification to a coloring of the configuration is called "initially good". For example, the single-vertex configuration above with 3 or less neighbors were initially good. In general, the surrounding graph must be systematically recolored to turn the ring's coloring into a good one, as was done in the case above where there were 4 neighbors; for a general configuration with a larger ring, this requires more complex techniques. Because of the large number of distinct four-colorings of the ring, this is the primary step requiring computer assistance.