Nearly neighbourly families of standard boxes

27 Jul 2016  ·  Bojarski Jacek, Kisielewicz Andrzej P., Przesławski Krzysztof ·

It is demonstrated that each nearly neighbourly family of standard boxes in $\mathbb{R}^3$ has at most 12 elements. A combinatorial classification of all such families that have exactly 12 elements is given... All families satisfying an extra property called incompressibility are described. Compressible families are discussed briefly. read more

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Combinatorics