Apex graphs with embeddings of face-width three (Q1377691)
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scientific article; zbMATH DE number 1109968
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Apex graphs with embeddings of face-width three |
scientific article; zbMATH DE number 1109968 |
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Apex graphs with embeddings of face-width three (English)
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26 January 1998
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An apex graph is a graph which has a vertex whose removal makes the resulting graph planar. The main result characterizes embeddings of apex graphs with face-width (representativity) three. The orientable genus of such embeddings can be arbitrarily high. The paper contains a short proof of a theorem of Robertson, Seymour and Thomas stating that any embedding of an apex graph in a nonorientable surface has face-width at most two.
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representativity
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apex graph
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embeddings
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face-width
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orientable genus
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