An exact cutting plane algorithm to solve the selective graph coloring problem in perfect graphs

We consider the selective graph coloring problem, which is a generalization of classical problem. Given together with partition its vertex set into clusters, we want to choose exactly one per cluster so that number colors needed color selected vertices minimized. This problem known be NP-hard. In this study, focus on an exact cutting plane algorithm for in perfect graphs. Since there exists no suite instances best our knowledge, also propose randomly (but not uniformly) generate graphs, and provide large collection available online. conduct computational experiments test method graphs varying size densities, compare results state-of-the-art from literature solving integer programming formulation by CPLEX. Our demonstrate solution strategy significantly improves solvability