Complexity Layers in Graph Coloring

The complexity of graph coloring instances falls into a continuum which extends from problem instances that can be solved easily by any algorithm to those which appear to defy solution by any known polynomial algorithm. Since the general problem appears to be intractable many efforts to date have tried to solve some subset of the problem space. This investigation shows how the observed continuum of complexity can be represented as layers of complexity by defining a general algorithm that has the ability to scale in a natural way from O(n(2)),O(n(3)),O(n(4)), etc. Each increase in complexity adds a new layer of problems that can be solved.