Algorithmic point

Use Dilworth’s theorem to derive the marriage theorem. We remark that our proof of Theorem 7.5.2 is also interesting from an algorithmic point of view, since it allows to calculate the Dilworth number of G by determining a maximal matching in the bipartite graph H, because of Δ = n − α_(H). Thus Theorem 7.5.2 implies the following result (and its translation to posets which we will leave to the reader).