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 Tr. Mat. Inst. Steklova, 2015, Volume 288, Pages 133–148 (Mi tm3612)

Extremal problems of circle packings on a sphere and irreducible contact graphs

O. R. Musinab, A. S. Tarasova

a Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow, Russia
b University of Texas at Brownsville, Brownsville, TX, USA

Abstract: Recently, we have enumerated (up to isometry) all locally rigid packings of congruent circles (spherical caps) on the unit sphere with the number of circles $N<12$. This problem is equivalent to the enumeration of irreducible spherical contact graphs. In this paper, we show that using the list of irreducible contact graphs, one can solve various problems on extremal packings such as the Tammes problem for the sphere and projective plane, the problem of the maximum kissing number in spherical packings, Danzer's problems, and other problems on irreducible contact graphs.

 Funding Agency Grant Number National Science Foundation DMS-1400876 Russian Foundation for Basic Research 13-01-12458, 15-01-99563

DOI: https://doi.org/10.1134/S0371968515010094

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English version:
Proceedings of the Steklov Institute of Mathematics, 2015, 288, 117–131

Bibliographic databases:

UDC: 519.146

Citation: O. R. Musin, A. S. Tarasov, “Extremal problems of circle packings on a sphere and irreducible contact graphs”, Geometry, topology, and applications, Collected papers. Dedicated to Professor Nikolai Petrovich Dolbilin on the occasion of his 70th birthday, Tr. Mat. Inst. Steklova, 288, MAIK Nauka/Interperiodica, Moscow, 2015, 133–148; Proc. Steklov Inst. Math., 288 (2015), 117–131

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/tm3612
• https://doi.org/10.1134/S0371968515010094
• http://mi.mathnet.ru/eng/tm/v288/p133

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. E. N. Sosov, “Special metric invariants”, Lobachevskii J. Math., 39:2, 3, SI (2018), 286–288
2. O. R. Musin, “Towards a proof of the 24-cell conjecture”, Acta Math. Hung., 155:1 (2018), 184–199
3. Musin O.R., “Graphs and Spherical Two-Distance Sets”, Eur. J. Comb., 80 (2019), 311–325
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