On Simplices in Diameter Graphs in R-4

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.


Published in:
Mathematical Notes, 101, 1-2, 265-276
Year:
2017
Publisher:
New York, Maik Nauka/Interperiodica/Springer
ISSN:
0001-4346
Keywords:
Laboratories:




 Record created 2017-05-01, last modified 2018-03-17


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