A graph coloring approach for channel assignment in cellular network via propositional satisfiability

Graph Colorability Problem (GCP) is a well known NP-Complete problem consisting on finding the k minimum number of colors to paint the vertexes of a graph in such a way that two adjacent vertexes joined by an edge has always different colors. GCP is very important because it has many applications; one of the great application in cellular network is channel assignment. Efficient Channel assignment is a big challenge in cellular network. Here, a cellular network is modeled as graph, set of channels (colors) must be assigned to cells (vertices) while avoiding interference. Since, till now there are not any known deterministic methods that can solved a GCP in a polynomial time. But with the help of polynomial solvability of 3-SAT, we can solved GCP into polynomial time. In this paper, we transformed GCP into a 3-CNF-Satisfiability Problem. Further, we illustrate it by one of the instance of graph coloring, the 3-colorable graph into 3-CNF-SAT.