Abstract
We prove a min-max result on special partially ordered sets, a conjecture of András Frank. As corollaries we deduce Dilworth's theorem and the well-known min-max formula for the minimum size edge cover of a graph.
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References
C. Berge: Sur le couplage maximum d'un graphe,Comptes Rentus Hebdomadaires des Séances de l'Académie des Sciences [Paris],247 (1958) 258–259.
R. P. Dilworth: A decomposition theorem for partially ordered sets,Annals of Mathematics,51 (1950) 161–166.
J. Edmonds: Paths, tress, and flowers,Canadian Journal of Mathematics,17 (1965) 449–467.
A. Frank: personal communication
T. Gallai: Neuer Beweis eines Tutte'schen Satzes,A Magyar Tudományos Akadémia Matematikai Kutató Intézetének Közleményei,8 (1963) 373–395.
T. Gallai: Maximale Systeme unabhängiger Kanten,A Magyar Tudományos Akadémia Matematikai Kutató Intézetének Közleményei,9 (1964) 401–413.
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Research supported by the Netherlands Organization for Scientific Research (NWO)
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Fleiner, T. Covering a symmetric poset by symmetric chains. Combinatorica 17, 339–344 (1997). https://doi.org/10.1007/BF01215916
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DOI: https://doi.org/10.1007/BF01215916