Abstract
Given an element x of a partial order P, a set S ⊂ P is said to be a cutset for x if S ∪ x meets every maximal chain of P and x is incomparable to every element of S. The cutset number of P is the minimum m such that every element of P has a cutset of size at most m. Let w(m, h) be the maximum width of a poset with height h and cutset number m. We determine the order of growth of w(m, h) for fixed m or fixed h: w(m, h)∈Θ(h ⌊m/2⌋) for fixed m and w(m, h)∈Θ(m h) for fixed h.
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Communicated by I. Rival
Research supported in part by ONR Grant N00014-85K0570 and by NSA/MSP Grant MDA904-90-H-4011.
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Kézdy, A., Markert, M. & West, D.B. Wide posets with fixed height and cutset number. Order 7, 115–132 (1990). https://doi.org/10.1007/BF00383761
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DOI: https://doi.org/10.1007/BF00383761