Contact graphs of ball packings

Abstract

A contact graph of a packing of closed balls is a graph with balls as vertices and pairs of tangent balls as edges. We prove that the average degree of the contact graph of a packing of balls (with possibly different radii) in ${\mathbb{R}}^3$ is not greater than $13.92$. We also find new upper bounds for the average degree of contact graphs in ${\mathbb{R}}^4$ and ${\mathbb{R}}^5$.

References in corpus (5)

• New upper bounds for kissing numbers from semidefinite programming
• Lattices with exponentially large kissing numbers
• Spaces of convex n-partitions
• Ball packings with high chromatic numbers from strongly regular graphs
• Semidefinite programming bounds for the average kissing number

Cited by in corpus (2)

• Kissing number in non-Euclidean spaces of constant sectional curvature
• Kissing number in hyperbolic space