“Poly-unsaturated” posets: The Greene-Kleitman theorem is best possible
نویسندگان
چکیده
منابع مشابه
Polyunsaturated posets and graphs and the Greene-Kleitman theorem
A partition of a finite poset into chains places a natural upper bound on the size of a union of k antichains. A chain partition is k-saturated if this bound is achieved. Greene and Kleitman [9] proved that, for each k, every finite poset has a simultaneously kand k + 1-saturated chain partition. West [15] showed that the Greene-Kleitman Theorem is best-possible in a strong sense by exhibiting,...
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The celebrated Dilworth theorem (Ann. of Math. 5 1 (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. 2 1 (1960), 18 l-186) we prove a theorem on acyclic digraphs which contains the Greene-Kleitman theorem. The method of proof is derived from M. Saks’ elegant pr...
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Aharoni, R. and I. Ben-Arroyo Hartman, On Greene-Kleitman’s theorem for general digraphs, Discrete Mathematics 120 (1993) 13-24. Linial conjectured that Greene-Kleitman’s theorem can be extended to general digraphs. We prove a stronger conjecture of Berge for digraphs having k-optimal path partitions consisting of ‘long’ paths. The same method yields known results for acyclic digraphs, and exte...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1986
ISSN: 0097-3165
DOI: 10.1016/0097-3165(86)90118-4