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