Document Type

Article

Publication Date

11-2020

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 R3 is not greater than 13.955. We also find new upper bounds for the average degree of contact graphs in R4 and R5.

Comments

© 2020 Elsevier Inc. All rights reserved. Original published version available at https://doi.org/10.1016/j.jctb.2020.05.007

Creative Commons License

Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

First Page

323

Last Page

340

Publication Title

Journal of Combinatorial Theory, Series B

DOI

10.1016/j.jctb.2020.05.007

Included in

Mathematics Commons

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