Abstract
SupposeG is a finite connected graph. LetC(G) denote the inclusion ordering on the connected vertex-induced subgraphs ofG. Penrice asked whetherC(G) is Sperner for general graphsG. Answering Penrice's question in the negative, we present a treeT such thatC(T) is not Sperner. We also construct a related distributive lattice that is not Sperner.
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Communicated by D. Duffus
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Jacobson, M.S., Kézdy, A.E. & Seif, S. The poset on connected induced subgraphs of a graph need not be Sperner. Order 12, 315–318 (1995). https://doi.org/10.1007/BF01111746
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DOI: https://doi.org/10.1007/BF01111746