The structure of the planar triangulations in terms of bundles and stars (Q2760687)
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scientific article; zbMATH DE number 1682229
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The structure of the planar triangulations in terms of bundles and stars |
scientific article; zbMATH DE number 1682229 |
Statements
13 December 2001
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Kotzig theorem
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star weight
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plane map
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planar graph
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plane triangulation
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0.87643373
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0.8714558
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0.86432976
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0.86333895
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0.86333895
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0.86129403
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The structure of the planar triangulations in terms of bundles and stars (English)
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The weight of a precomplete star of a vertex \(v\) of a plane map \(G\) is the sum of the degrees of the vertices of \(G\) adjacent to \(v\) except the vertex having the maximal degree among them. It is shown that if a plane triangulation does not contain any sufficiently long chains of vertices of degree 4 then it contains a bounded weight precomplete star of a vertex of degree at most 5. The authors propose to use this result in forthcoming papers to obtain the best possible upper bounds for the 2-distance degree and 2-distance chromatic number of an arbitrary planar graph.
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