A simple way to tell a simple polytope from its graph (Q1120602)
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scientific article; zbMATH DE number 4101271
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A simple way to tell a simple polytope from its graph |
scientific article; zbMATH DE number 4101271 |
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A simple way to tell a simple polytope from its graph (English)
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1988
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Let P be a simple d-dimensional polytope and G(P) be the graph of P. Two vertices u and v in V(P) are adjacent in G(P) if [v,u] is a 1-dimensional face of P. Recently, \textit{R. Blind} and \textit{P. Mani-Levitska} [Aequationes Math. 34, 287-297 (1987; Zbl 0634.52005)] proved a conjecture of Perles that G(P) determines the entire combinatorial structure of P. In this note the author gives a simple proof of this result.
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acyclic orientation
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regular graph
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polytope
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