This article describes eight formulations for the generalized minimum spanning tree problem (gmstp). Relationships between the polytopes of their linear relaxations are established. It is shown that four of these polytopes are strictly included in the remaining ones. This analysis suggests which formulations should be preferred for the construction of a branch-and-cut algorithm and for the evaluation of heuristics.
Feremans, C., Labbé, M., & Laporte, G. (2002). A Comparative Analysis of Several Forumulations for the Generalized Minimum Spanning Tree Problem. Networks, 39(1), 29-34. https://doi.org/10.1002/net.10009