  A theory about the implication structure in graph coloring is presented.
Discovering hidden relations is a crucial activity in every scientific
discipline. The development of mathematical models to study and discover such
hidden relations is of the most highest interest. The main contribution
presented in this work is a model of hidden relations materialized as
implicit-edges and implicit-identities in the graph coloring problem, these
relations can be interpreted in physical and chemical models as hidden forces,
hidden interactions, hidden reactions or hidden variables. Also this theory can
be extended to the complete class of NP-complete problems.
