Subdivisions in planar graphs (Q1366603)
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scientific article; zbMATH DE number 1060746
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Subdivisions in planar graphs |
scientific article; zbMATH DE number 1060746 |
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Subdivisions in planar graphs (English)
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15 September 1997
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Given four distinct vertices in a 4-connected planar graph \(G\), we characterize when the graph \(G\) contains a \(K_4\)-subdivision with the given vertices as its degree three vertices. This result implies the following conjecture of Robertson and Thomas: a 5-connected planar graph has no \(K_4\)-subdivision with specified degree three vertices, if and only if, the four specified vertices are contained in a facial cycle in the unique plane embedding of the graph.
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disjoint paths
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subdivisions
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connectivity
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planar graph
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plane embedding
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0.9153365
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0.91235006
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0.9066214
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