Searching for a cycle with maximum coverage in undirected graphs

The present contribution considers the problem of identifying a simple cycle in an undirected graph such that the number of nodes in the cycle or adjacent to it, is maximum. This problem is denoted as the Maximum Covering Cycle Problem and it is shown to be NP-complete. We present an iterative procedure that, although it cannot be shown to be polynomial, yields (in practice) high-quality solutions within reasonable time on graphs of moderate density.