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Matematicheskie Zametki, 2010, Volume 87, Issue 2, Pages 233–245
DOI: https://doi.org/10.4213/mzm5188 (Mi mzm5188) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Partition of Three-Dimensional Sets into Five Parts of Smaller Diameter

A. B. Kupavskii, A. M. Raigorodskii

M. V. Lomonosov Moscow State University
Full-text PDF (555 kB) Citations (6)
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DOI: https://doi.org/10.4213/mzm5188
Abstract: The classical Borsuk problem on partitioning sets into pieces of smaller diameter is considered. A new upper bound for
d35=supΦ⊂R3,diamΦ=1inf{x⩾0:Φ=Φ1∪Φ2∪⋯∪Φ5,diamΦi⩽x}
is given, which improves the previous bound obtained by Lassak in 1982.
Keywords: Borsuk's problem, partition of 3D sets, diameter of a set, Lassak's bound, Gale's conjecture, Jung's ball, Helly's theorem, isometry.
Received: 04.06.2008
English version:
Mathematical Notes, 2010, Volume 87, Issue 2, Pages 218–229
DOI: https://doi.org/10.1134/S0001434610010281
Bibliographic databases:
UDC: 514.17
Language: Russian
Citation: A. B. Kupavskii, A. M. Raigorodskii, “Partition of Three-Dimensional Sets into Five Parts of Smaller Diameter”, Mat. Zametki, 87:2 (2010), 233–245; Math. Notes, 87:2 (2010), 218–229
Citation in format AMSBIB
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    • This publication is cited in the following 6 articles:
    1. Arthur Bikeev, “Borsuk's problem, Boltyanski's illumination problem, and circumradius”, Moscow J. Comb. Number Th., 12:3 (2023), 223  crossref
    2. V. A. Voronov, A. D. Tolmachev, D. S. Protasov, A. M. Neopryatnaya, Communications in Computer and Information Science, 1881, Mathematical Optimization Theory and Operations Research: Recent Trends, 2023, 391  crossref
    3. Lian Ya., Wu S., “Partition Bounded Sets Into Sets Having Smaller Diameters”, Results Math., 76:3 (2021), 116  crossref  mathscinet  isi
    4. V. P. Filimonov, “Covering sets in Rm”, Sb. Math., 205:8 (2014), 1160–1200  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    5. Raigorodskii A.M., “Predislovie redaktora nomera”, Trudy MFTI, 4:1-13 (2012), 4–11  elib
    6. Bulankina V.V., “O razbienii ploskikh mnozhestv na pyat chastei bez rasstoyaniya √2−√3”, Trudy MFTI, 4:1-13 (2012), 56–72  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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