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 - http://www.scopus.com/inward/record.url?scp=0007113773&partnerID=8YFLogxK
U2 - 10.1016/0097-3165(81)90029-7
DO - 10.1016/0097-3165(81)90029-7
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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 -