# Has the concept of TU other application than proving convex hull characterizations?

If a matrix is totally unimodular (TU), then we know that $$\text{\{}x| Ax\leq b \text{\}}$$ is integral for all integral $$b$$'s. This is often used for convex hull proofs, but does the concept of TU has further applications?

Total unimodularity is a strong property that guarantees integer optimal solutions to an LP problem for all $$c$$ and integer $$b$$. Many IP models for which the matrix $$A$$ is not totally unimodular frequently (although not always) produce integer solutions to the optimal solution of the corresponding LP problem.