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research article
On Simplices in Diameter Graphs in R-4
Kupavskii, A. B.
•
Polyanskii, A. A.
2017
A graph G is a diameter graph in R-d if its vertex set is a finite subset in R-d of diameter 1 and edges join pairs of vertices a unit distance apart. It is shown that if a diameter graph G in R-4 contains the complete subgraph K on five vertices, then any triangle in G shares a vertex with K. The geometric interpretation of this statement is as follows. Given any regular unit simplex on five vertices and any regular unit triangle in R-4, then either the simplex and the triangle have a common vertex or the diameter of the union of their vertex sets is strictly greater than 1.
Type
research article
Web of Science ID
WOS:000396392700031
Authors
Kupavskii, A. B.
•
Polyanskii, A. A.
Publication date
2017
Publisher
Published in
Volume
101
Issue
1-2
Start page
265
End page
276
Peer reviewed
REVIEWED
EPFL units
Available on Infoscience
May 1, 2017
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