On the chromatic number of graphs

Computing the chromatic number of a graph is an NP-hard problem. For random graphs and some other classes of graphs, estimators of the expected chroma tic number have been well studied. In this paper, a new 0-1 integer program ming formulation for the graph coloring problem is presented. The proposed new formulation is used to develop a method that generates graphs of known chromatic number by using the KKT optimality conditions of a related contin uous nonlinear program.