Formulating and Solving the Minimum Dominating Cycle Problem Abilio Lucena 1 Departamento de Administra¸ c˜ ao / PESC-COPPE Universidade Federal do Rio de Janeiro Rio de Janeiro, Brazil Alexandre Salles da Cunha Departamento de Ciˆ encia da Computa¸ c˜ ao Universidade Federal de Minas Gerais Belo Horizonte, Brazil Luidi Simonetti Instituto de Computa¸ c˜ ao Universidade Federal Fluminense Niteroi, Brazil Abstract This paper introduces a formulation for the Minimum Dominating Cycle Problem. Additionally, a Branch and Cut algorithm, based on that formulation, is also inves- tigated. So far, the algorithm contains no primal heuristics. However, it managed to solve to proven optimality, in acceptable CPU times, all test instances with up to 120 vertices. Keywords: Minimum Dominating Cycle Problem, Formulations, Valid Inequalities, Branch and Cut Algorithm. Available online at www.sciencedirect.com Electronic Notes in Discrete Mathematics 41 (2013) 423–430 1571-0653/$ – see front matter © 2013 Elsevier B.V. All rights reserved. www.elsevier.com/locate/endm http://dx.doi.org/10.1016/j.endm.2013.05.121