On circle containment orders (Q1117256)
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scientific article; zbMATH DE number 4091570
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On circle containment orders |
scientific article; zbMATH DE number 4091570 |
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On circle containment orders (English)
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1988
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A partially ordered set is called a circle containment order provided it is isomorphic to a poset of circles in the plane ordered by inclusion. In this paper it is shown that the infinite three-dimensional poset \({\mathcal Z}^ 3\) is not a circle containment order. This fact contrasts with the conjecture that every finite three-dimensional poset is a circle order.
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circle containment order
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poset
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