Abstract
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 chromatic number have been well studied. In this paper, a new 0–1 integer programming 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 continuous nonlinear program.
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