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

This article is cited in 3 scientific papers (total in 3 papers)

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

Full text: PDF file (276 kB)
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English version:
Proceedings of the Steklov Institute of Mathematics, 2015, 288, 117–131

Bibliographic databases:

UDC: 519.146
Received in June 2014

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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\by O.~R.~Musin, A.~S.~Tarasov
\paper Extremal problems of circle packings on a~sphere and irreducible contact graphs
\inbook Geometry, topology, and applications
\bookinfo Collected papers. Dedicated to Professor Nikolai Petrovich Dolbilin on the occasion of his 70th birthday
\serial Tr. Mat. Inst. Steklova
\yr 2015
\vol 288
\pages 133--148
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm3612}
\crossref{https://doi.org/10.1134/S0371968515010094}
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\jour Proc. Steklov Inst. Math.
\yr 2015
\vol 288
\pages 117--131
\crossref{https://doi.org/10.1134/S0081543815010095}
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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  crossref  mathscinet  zmath  isi  scopus
    2. O. R. Musin, “Towards a proof of the 24-cell conjecture”, Acta Math. Hung., 155:1 (2018), 184–199  crossref  mathscinet  isi  scopus
    3. Musin O.R., “Graphs and Spherical Two-Distance Sets”, Eur. J. Comb., 80 (2019), 311–325  crossref  isi
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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