English

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

Metric Geometry 2015-04-21 v1 Combinatorics

Abstract

Recently, we enumerate up to isometry, all locally rigid circle packings on the unit sphere with number of circles N<12. This problem is equivalent to the enumeration of irreducible contact graphs. In this paper we show that by using the list of irreducible graphs can solve various problems of extreme packings such as the Tammes problem for the sphere and the projective plane, the maximal contacts problem, Danzer's and other problems on irreducible contact graphs.

Keywords

Cite

@article{arxiv.1410.0744,
  title  = {Extreme problems of circle packings on a sphere and irreducible contact graphs},
  author = {Oleg R. Musin and Alexey S. Tarasov},
  journal= {arXiv preprint arXiv:1410.0744},
  year   = {2015}
}

Comments

21 pages, 86 figures, in Russian