The Rainbow Cycle Cover Problem

We model and solve the Rainbow Cycle Cover Problem (RCCP). Given a connected and undirected graph G = (V,E,L) and a coloring function l that assigns a color to each edge of G from the finite color set L, a cycle whose edges have all different colors is called a rainbow cycle. The RCCP consists of finding the minimum number of disjoint rainbow cycles covering G. The RCCP on general graphs is known to be NP-complete. We model the RCCP as an integer linear program, we derive valid inequalities and we solve it by branch-and-cut. Computational results are reported on randomly generated instances.