Abstract
The celebrated Dilworth theorem ( Ann. of Math. 51 (1950), 161–166) on the decomposition of finite posets was extended by Greene and Kleitman ( J. Combin. Theory Ser. A 20 (1976), 41–68). Using the Gallai-Milgram theorem ( Acta Sci. Math. 21 (1960), 181–186) we prove a theorem on acyclic digraphs which contains the Greene-Kleitman theorem. The method of proof is derived from M. Saks' elegant proof ( Adv. in Math. 33 (1979), 207–211) of the Greene-Kleitman theorem.
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