2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/132829We analyze the problem of discovering long cycles inside a graph. We propose and test two algorithms for this task. The first one is based on recent advances in statistical mechanics and relies on a message passing procedure. The second follows a more standard Monte Carlo Markov Chain strategy. Special attention is devoted to Hamiltonian cycles of (non-regular) random graphs of minimal connectivity equal to three.Statistical MechanicsDisordered Systems and Neural NetworksComputational ComplexityProbabilitytext