K5 and K3,3 are Toroidal Penny Graphs

2024/10/14 by Lorand, Cédric · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2410.10673

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 K5 and K_3,3 are penny graphs on the flat square torus.

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• Recognizing Penny and Marble Graphs is Hard for Existential Theory of the Reals

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