English

K5 and K3,3 are Toroidal Penny Graphs

Combinatorics 2024-10-15 v1 Geometric Topology

Abstract

In this article we emphasize on the connection between two fields of study that are Penny Graphs, and the Optimal Packing of Spheres on the Flat Torus. We give a brief litterature overview on related results in the fields of planar graphs, penny graphs, toroidal penny graphs and spherical codes.We also show that K5K5 and K3,3K_{3,3} are penny graphs on the flat square torus.

Cite

@article{arxiv.2410.10673,
  title  = {K5 and K3,3 are Toroidal Penny Graphs},
  author = {Cédric Lorand},
  journal= {arXiv preprint arXiv:2410.10673},
  year   = {2024}
}

Comments

8 pages, 6 figures

R2 v1 2026-06-28T19:20:52.724Z