Extending the Greene-Kleitman theorem to directed graphs

Nathan Linial

doi:10.1016/0097-3165(81)90029-7

Extending the Greene-Kleitman theorem to directed graphs

Nathan Linial^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

27 Scopus citations

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
Pages (from-to)	331-334
Number of pages	4
Journal	Journal of Combinatorial Theory - Series A
Volume	30
Issue number	3
DOIs	https://doi.org/10.1016/0097-3165(81)90029-7
State	Published - May 1981
Externally published	Yes

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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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AB - 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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Extending the Greene-Kleitman theorem to directed graphs

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