Contact graphs of unit sphere packings revisited

@article{Bezdek2012ContactGO,
title={Contact graphs of unit sphere packings revisited},
author={K{\'a}roly Bezdek and Samuel Reid},
journal={Journal of Geometry},
year={2012},
volume={104},
pages={57-83}
}
• Published 21 October 2012
• Mathematics
• Journal of Geometry
The contact graph of an arbitrary finite packing of unit balls in Euclidean 3-space is the (simple) graph whose vertices correspond to the packing elements and whose two vertices are connected by an edge if the corresponding two packing elements touch each other. One of the most basic questions on contact graphs is to find the maximum number of edges that a contact graph of a packing of n unit balls can have. In this paper, improving earlier estimates, we prove that the number of touching pairs…
27 Citations

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