Code and Data Repository for Branch-and-Cut Algorithms for Colorful Components Problems

We tackle three optimization problems in which a colored graph must be partitioned into connected colorful components. A component is colorful if all its vertices have different colors. We consider three different objectives, formulate the resulting problems as integer nonlinear programs and linearize them through standard linearization techniques. Then, we develop exact branch-and-cut algorithms, including families of valid inequalities for each problem, bounds reducing the size of the models, warm-start and preprocessing techniques.