General penny graphs are at most 43/18-dense

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.

13 pages, 21 figures; a few modifications based on the reviews

References in corpus (2)

• Combinatorial distance geometry in normed spaces
• Triangle-Free Penny Graphs: Degeneracy, Choosability, and Edge Count