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.
Original language | American English |
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Pages (from-to) | 331-334 |
Number of pages | 4 |
Journal | Journal of Combinatorial Theory - Series A |
Volume | 30 |
Issue number | 3 |
DOIs | |
State | Published - May 1981 |
Externally published | Yes |