PreprintCC BY 4.0arXiv
Linear crossing families via dual levels
Abstract
Building on the work of Pach, Rubin, and Tardos, we prove that every set of n≥2 points in the real plane with no three collinear contains at least cn pairwise crossing segments with distinct endpoints, for an absolute constant c>0.
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BibTeX
@misc{gehrunger2026linear,
title = {{Linear crossing families via dual levels}},
author = {Tim Gehrunger},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.29449},
eprint = {2609.29449},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.29449},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Linear crossing families via dual levels
AU - Tim Gehrunger
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.29449
UR - https://arxiv.org/abs/2609.29449
AB - Building on the work of Pach, Rubin, and Tardos, we prove that every set of n≥2 points in the real plane with no three collinear contains at least cn pairwise crossing segments with distinct endpoints, for an absolute constant c>0.
ER -