Nearly-neighborly families of tetrahedra and the decomposition of some multigraphs (Q1106468)
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scientific article; zbMATH DE number 4062044
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Nearly-neighborly families of tetrahedra and the decomposition of some multigraphs |
scientific article; zbMATH DE number 4062044 |
Statements
Nearly-neighborly families of tetrahedra and the decomposition of some multigraphs (English)
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1988
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Two d-polyhedra in \(E^ d\) are nearly-neighborly if they are separated by a hyperplane which contains a facet of each. The main result is: there can be at most 15 mutually nearly-neighborly tetrahedra in \(E^ 3\). There is a glossary of results on nearly-neighborly (and neighborly) sets of polyhedra, several conjectures, relevant results on decomposition of certain graphs. The paper ends with the following ``Note added in proof. Using a similar yet more detailed approach, S. Furino, B. Gamble and J. Zako (sic) proved that there can be at most 14 nearly-neighborly tetrahedra in \(E^ 3\).''
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Bagemihl's conjecture
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decomposition of graphs
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nearly-neighborly tetrahedra
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