Abstract : Intraspecific studies often make use of haplotype networks instead of gene genealogies to represent the evolution of a set of genes. Cassens et al. proposed one such network reconstruction method, based on the global maximum parsimony principle, which was later recast by the first author of the present work as the problem of finding a minimum common supergraph of a set of t partially labelled trees. Although algorithms were proposed for solving the problem on two graphs, the complexity of the general problem remains unknown. In this paper, we show that the corresponding decision problem is NP-complete for t = 3. We then propose a declarative programming approach to solving the problem to optimality in practice, as well as a heuristic approach, both based on the IDP system, and assess the performance of both methods on randomly generated data.