Extending the Greene-Kleitman theorem to directed graphs

Nathan Linial*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

27 Scopus citations


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 languageAmerican English
Pages (from-to)331-334
Number of pages4
JournalJournal of Combinatorial Theory. Series A
Issue number3
StatePublished - May 1981
Externally publishedYes


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