Acyclic Support Criterion for Transportation Polytopes is a result from the foundations of optimal transport. For mathematical objects, let mathematical objects and mathematical objects satisfy i=1m ai = j=1n bj. Let (a,b) := \P=(pij) [0,)m n : j=1n pij=ai i,\ i=1m pij=bj j\. For mathematical objects, define its suppor. It helps organize the relationship between Monge maps, Kantorovich plans, duality, and Wasserstein geometry.