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

29 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	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

Access to Document

10.1016/0097-3165(81)90029-7

Cite this

@article{3ac5da7ccfef4dc78e5af122bc45276f,

title = "Extending the Greene-Kleitman theorem to directed graphs",

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.",

author = "Nathan Linial",

year = "1981",

month = may,

doi = "10.1016/0097-3165(81)90029-7",

language = "אנגלית",

volume = "30",

pages = "331--334",

journal = "Journal of Combinatorial Theory. Series A",

issn = "0097-3165",

publisher = "Academic Press Inc.",

number = "3",

}

TY - JOUR

T1 - Extending the Greene-Kleitman theorem to directed graphs

AU - Linial, Nathan

PY - 1981/5

Y1 - 1981/5

N2 - 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.

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.

UR - https://www.scopus.com/pages/publications/0007113773

U2 - 10.1016/0097-3165(81)90029-7

DO - 10.1016/0097-3165(81)90029-7

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:0007113773

SN - 0097-3165

VL - 30

SP - 331

EP - 334

JO - Journal of Combinatorial Theory. Series A

JF - Journal of Combinatorial Theory. Series A

IS - 3

ER -

Extending the Greene-Kleitman theorem to directed graphs

Abstract

Access to Document

Other files and links

Fingerprint

Cite this