Shrinkability of minimal elements in sphere representations of posets (Q1368665)
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scientific article; zbMATH DE number 1067854
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Shrinkability of minimal elements in sphere representations of posets |
scientific article; zbMATH DE number 1067854 |
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Shrinkability of minimal elements in sphere representations of posets (English)
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1997
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As main results the authors prove the following theorems: 1. For every \(k\geq 2\) there exists a poset \(P= (X,\leq)\) so that \(P\) is a \(k\)-sphere order, but there is no \(k\)-sphere representation which assigns to every minimal element a ball of radius zero. 2. There exists a planar graph \(G\) so that no circle representation of \(P(G)\) has all vertices assigned to circles of radius zero.
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poset
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\(k\)-sphere order
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\(k\)-sphere representation
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ball of radius zero
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planar graph
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circle representation
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