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This article is cited in 5 scientific papers (total in 5 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.
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, Trudy Mat. Inst. Steklova, 288, MAIK Nauka/Interperiodica, Moscow, 2015, 133–148; Proc. Steklov Inst. Math., 288 (2015), 117–131
Linking options:
https://www.mathnet.ru/eng/tm3612https://doi.org/10.1134/S0371968515010094 https://www.mathnet.ru/eng/tm/v288/p133
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Abstract page: | 338 | Full-text PDF : | 102 | References: | 52 | First page: | 1 |
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