Nearly-neighborly families of tetrahedra and the decomposition of some multigraphs

Joseph Zaks

doi:10.1016/0097-3165(88)90001-5

Nearly-neighborly families of tetrahedra and the decomposition of some multigraphs

Joseph Zaks

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

A family of d-polyhedra in E^d is called nearly-neighborly if every two members are separated by a hyperplane which contains facets of both of them. Reducing the known upper bound by 1, we prove that there can be at most 15 members in a nearly-neighborly family of tetrahedra in E³. The proof uses the following statement: "If the graph, obtained from K₁₆ by duplicating the edges of a 1-factor, is decomposed into t complete bipartite graphs, then t ≥ 9." Similar results are derived for various graphs and multigraphs.

Original language	English
Pages (from-to)	147-155
Number of pages	9
Journal	Journal of Combinatorial Theory. Series A
Volume	48
Issue number	2
DOIs	https://doi.org/10.1016/0097-3165(88)90001-5
State	Published - Jul 1988

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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abstract = "A family of d-polyhedra in Ed is called nearly-neighborly if every two members are separated by a hyperplane which contains facets of both of them. Reducing the known upper bound by 1, we prove that there can be at most 15 members in a nearly-neighborly family of tetrahedra in E3. The proof uses the following statement: {"}If the graph, obtained from K16 by duplicating the edges of a 1-factor, is decomposed into t complete bipartite graphs, then t ≥ 9.{"} Similar results are derived for various graphs and multigraphs.",

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AB - A family of d-polyhedra in Ed is called nearly-neighborly if every two members are separated by a hyperplane which contains facets of both of them. Reducing the known upper bound by 1, we prove that there can be at most 15 members in a nearly-neighborly family of tetrahedra in E3. The proof uses the following statement: "If the graph, obtained from K16 by duplicating the edges of a 1-factor, is decomposed into t complete bipartite graphs, then t ≥ 9." Similar results are derived for various graphs and multigraphs.

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Nearly-neighborly families of tetrahedra and the decomposition of some multigraphs

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