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.
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics