Convex representations of maps on the torus and other flat surfaces (Q1314444)
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scientific article; zbMATH DE number 502909
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Convex representations of maps on the torus and other flat surfaces |
scientific article; zbMATH DE number 502909 |
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Convex representations of maps on the torus and other flat surfaces (English)
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16 February 1994
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It is shown that every map on a torus has a convex representation if and only if it is reduced. This property is a generalization of 3- connectedness of the corresponding graph. It is also shown that reduced maps on a Klein bottle, a cylinder, or a Möbius band have convex representations on the corresponding flat surfaces. The algorithm for constructing these maps is shown to be a linear-time algorithm.
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Stein-Tutte theorem
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map on a torus
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convex representation
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3- connectedness
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Klein bottle
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cylinder
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Möbius band
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flat surfaces
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linear-time algorithm
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