Representing graphs by sphere packings
Oleg Rustumovich Musin · Open Collections · 2017
Any graph G can be embedded in a Euclidean space as a contact graph of sphere packing. In this talk we consider contact graphs of packings by congruent spheres in Euclidean and spherical spaces. In particular, we compute explicitly the minimal dimensions of representations for the join of graphs. We also show that analogs of Steiner's porism and Soddy's hexlet in higher dimensions can be found via packings by congruent spheres of spherical spaces.