The poset on connected induced subgraphs of a graph need not be Sperner |
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| Authors: | Michael S Jacobson André E Kézdy Steve Seif |
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| Institution: | (1) Department of Mathematics, University of Louisville, 40292 Louisville, KY, USA |
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| 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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| Keywords: | 06A06 |
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