The stable marriage polytope is the convex hull of the incidence vectors of the stable matchings in a bipartite graph whose vertices have strict preferences over their incident edges. An unmatched pair is blocking when both endpoints prefer each other to their assignments, with being unmatched worse than any acceptable partner (Barbato and Lancini 2026).
Barbato and Lancini (2026) proved that the stable marriage polytope has box-total dual integrality. Thus it admits a system of linear inequalities whose total dual integrality is preserved after adding arbitrary rational coordinate bounds. They also proved that Rothblum's defining system itself has this property.
