Quadrangulations on closed surfaces (Q2780954)
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scientific article; zbMATH DE number 1720153
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Quadrangulations on closed surfaces |
scientific article; zbMATH DE number 1720153 |
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21 April 2002
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closed surfaces
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quadrilateral imbeddings
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2-manifolds
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diagonal transformations
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0.9264566
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0.9241545
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0.9147263
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0.9111693
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0.90717536
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Quadrangulations on closed surfaces (English)
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The author surveys work on quadrilateral imbeddings of graphs in closed 2-manifolds, focusing on diagonal transformations of two types: (1) a diagonal slide replaces quadrilaterals \(cfabc\) and \(fcdef\) with quadrilaterals \(adefa\) and \(dabcd\); (2) a diagonal rotation replaces quadrilaterals \(cvabc\) and \(avcda\) with quadrilaterals \(bvdab\) and \(dvbcd\). The work is motivated by attempts to find an analogy, for quadrilateral imbeddings, to a result by \textit{S. Negami} [Discrete Math. 135, 225-232 (1994; Zbl 0823.05028)] concerning the equivalence (under finite sequences of diagonal flips) of triangular imbeddings.
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