2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/72270Morse matchings capture the essential structural information of discrete Morse functions. We show that computing optimal Morse matchings is NP-hard and give an integer programming formulation for the problem. Then we present polyhedral results for the corresponding polytope and report on computational results.CombinatoricsOptimization and Control90C27 (06A07, 52B99, 57Q05, 57R70)text