  The Total Matching Polytope generalizes the Stable Set Polytope and the
Matching Polytope. In this paper, we give the perfect formulation for Trees and
we derive two new families of valid inequalities, the balanced biclique
inequalities which are always facet-defining and the non-balanced lifted
biclique inequalities obtained by a lifting procedure, which are facet-defining
for bipartite graphs. Finally, we give a complete description for Complete
Bipartite Graphs.
