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

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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.

Original languageEnglish
Pages (from-to)147-155
Number of pages9
JournalJournal of Combinatorial Theory. Series A
Issue number2
StatePublished - Jul 1988

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics


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