The graph coloring problem is a notoriously hard problem, for which we do not have efficient algorithms. A coloring of a graph is an assignment of colors to its vertices such that the end points of every edge have different colors. A k-coloring is a coloring that uses at most k distinct colors. The graph coloring problem is to find a coloring that uses the minimum number of colors. Given a 3-colorable graph, the best known efficient algorithms output an n0. 199···-coloring. It is known that efficient algorithms cannot find a 4-coloring, assuming …