Stationary straight-line representations of stationary random graphs (Q1904408)
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scientific article; zbMATH DE number 828206
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Stationary straight-line representations of stationary random graphs |
scientific article; zbMATH DE number 828206 |
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Stationary straight-line representations of stationary random graphs (English)
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30 May 1996
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The authors introduce a new concept of a planar random graph. It is called stationary if its finite-dimensional distributions are invariant under translation. With this terminology they prove that there exists a stationary planar graph which does not have a stationary straight-line representation. Thus the theorem on straight-line representations of planar graphs proved by K. Wagner and I. Fary in the finite case and by the reviewer in the infinite case does not extend to this probabilistic framework.
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planar random graph
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stationary planar graph
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stationary straight-line representation
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0.7532452344894409
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0.7357567548751831
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