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Generalization of Dilworth's Theorem on Minimal Chain Decomposition

Author

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  • M. Raghavachari

    (Carnegie-Mellon University)

  • V. L. Mote

    (Indian Institute of Management, Ahmedabad)

Abstract

The decomposition of a finite partially ordered set of elements as a union of chains was considered by Dilworth [2]. Dantzig and Hoffman [1] formulated this problem as a linear programming problem and obtained Dilworth's theorem from duality theory. For some practical applications and for a method to obtain a minimal decomposition see Ford and Fulkerson [3]. In this paper we generalize this problem to the case when the set is not necessarily partially ordered and obtain a method of finding a minimal chain decomposition of the set.

Suggested Citation

  • M. Raghavachari & V. L. Mote, 1970. "Generalization of Dilworth's Theorem on Minimal Chain Decomposition," Management Science, INFORMS, vol. 16(7), pages 508-511, March.
    • Handle: RePEc:inm:ormnsc:v:16:y:1970:i:7:p:508-511
    DOI: 10.1287/mnsc.16.7.508
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