Geodesic
Nearly neighbourly families of standard boxes
Jacek Bojarski1 ; Andrzej Piotr Kisielewicz1 ; Krzysztof Przesławski1
1Wydział Matematyki, Informatyki i Ekonometrii, Uniwersytet Zielonogorski
The electronic journal of combinatorics, Tome 26 (2019) no. 4
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It is shown 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 the families satisfying an extra property called incompressibility are described. Compressible families are discussed briefly.
DOI : 10.37236/6771
Classification : 52B10, 05C69
Mots-clés : box, nearly neighborly position

Jacek Bojarski  1   ; Andrzej Piotr Kisielewicz  1   ; Krzysztof Przesławski  1

1 Wydział Matematyki, Informatyki i Ekonometrii, Uniwersytet Zielonogorski 
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     title = {Nearly neighbourly families of standard boxes},
     journal = {The electronic journal of combinatorics},
     year = {2019},
     volume = {26},
     number = {4},
     doi = {10.37236/6771},
     zbl = {1475.52016},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/6771/}
}
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Jacek Bojarski; Andrzej Piotr Kisielewicz; Krzysztof Przesławski. Nearly neighbourly families of standard boxes. The electronic journal of combinatorics, Tome 26 (2019) no. 4. doi: 10.37236/6771

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