Bounds on Borsuk Numbers in Distance Graphs of a Special Type

In 1933, Borsuk stated a conjecture, which has become classical, that the minimum number of parts of smaller diameter into which an arbitrary set of diameter 1 in can be partitioned is . In 1993, this conjecture was disproved using sets of points with coordinates 0 and 1. Later, the second author ob...

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Bibliographic Details
Published inProblems of information transmission Vol. 57; no. 2; pp. 136 - 142
Main Authors Berdnikov, A. V., Raigorodskii, A.M.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.04.2021
Springer Nature B.V
Subjects
639/301/1034/1035
639/925/357/995
Communications Engineering
Control
Electrical Engineering
Engineering
Information Storage and Retrieval
Large Systems
Lower bounds
Networks
Systems Theory
partitions
Borsuk’s problem
colorings
diameter graphs
(0, 1)-vectors
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Summary:In 1933, Borsuk stated a conjecture, which has become classical, that the minimum number of parts of smaller diameter into which an arbitrary set of diameter 1 in can be partitioned is . In 1993, this conjecture was disproved using sets of points with coordinates 0 and 1. Later, the second author obtained stronger counterexamples based on families of points with coordinates , , and . We establish new lower bounds for Borsuk numbers in families of this type.
ISSN:0032-9460
1608-3253
DOI:10.1134/S0032946021020034