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arXiv · 2402.09131

General penny graphs are at most 43/18-dense

Arsenii Sagdeev
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Abstract

We prove that among $n$ points in the plane in general position, the shortest distance occurs at most $43n/18$ times, improving upon the upper bound of $17n/7$ obtained by Tóth in 1997.

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Arsenii Sagdeev. 2024-11-19. General penny graphs are at most 43/18-dense. https://doi.org/10.2140/cnt.2025.14.75

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