Abstract
It is shown that if a chain complete ordered set does not have k+1 pairwise disjoint maximal chains for some finite k, then the minimum size of a cutset is equal to the maximum size of a collection of pairwise disjoint maximal chains. This answers a question of Pouzet and Zaguia.
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References
Brochet and M. Pouzet (1986) Maximal chains and cutsets of an ordered set: A Menger type approach, preprint.
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N. Zaguia (1985) Schedules, Cutsets, and Ordered Sets, PhD thesis, University of Calgary.
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Communicated by I. Rival
The author was supported in part by ONR grant N00014-85K-0494 and NSERC grants 69-3378, 69-0259, and 69-1325.
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Kierstead, H.A. A minimax theorem for chain complete ordered sets. Order 5, 75–83 (1988). https://doi.org/10.1007/BF00143899
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DOI: https://doi.org/10.1007/BF00143899