Abstract
Let F be a partially ordered set (poset). A poset P is called F-free if P contains no subposet isomorphic to F. A finite poset F is said to have the maximal element property if every maximal F-free subposet of any finite poset P contains a maximal element of P. It is shown that a poset F with at least two elements has the maximal element property if and only if F is an antichain or F ≅ 2 + 2.
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The research of both authors was supported by NSERC Discovery Grant 69-1926. Some of the results in this paper are contained in the thesis [5] of the second author.
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Sands, B., Shen, J. When Will Every Maximal F-free Subposet Contain a Maximal Element?. Order 27, 23–40 (2010). https://doi.org/10.1007/s11083-009-9136-6
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DOI: https://doi.org/10.1007/s11083-009-9136-6