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 T\'oth in 1997.
@article{arxiv.2402.09131,
title = {General penny graphs are at most 43/18-dense},
author = {Arsenii Sagdeev},
journal= {arXiv preprint arXiv:2402.09131},
year = {2025}
}
Comments
13 pages, 21 figures; a few modifications based on the reviews