Some remarks on the midrange crossing constant
Combinatorics
2019-07-02 v1
Abstract
We verify an upper bound of Pach and T\'oth [Combinatorica 17(1997), 427-439, Discrete and Computational Geometry 36(2006), 527-552] on the midrange crossing constant. Details of their upper bound have not been available. Our verification is different from their method and hinges on a result of Moon [J. Soc. Indust. Appl. Math. 13(1965), 506-510]. As Moon's result is optimal, we raise the question whether the midrange crossing constant is .
Cite
@article{arxiv.1907.00368,
title = {Some remarks on the midrange crossing constant},
author = {É. Czabarka and I. Singgih and L. A. Székely and Zhiyu Wang},
journal= {arXiv preprint arXiv:1907.00368},
year = {2019}
}