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arXiv · 2609.29449

Linear crossing families via dual levels

Tim Gehrunger
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Abstract

Building on the work of Pach, Rubin, and Tardos, we prove that every set of $n\ge2$ 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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Tim Gehrunger. 2026-09-24. Linear crossing families via dual levels. https://arxiv.org/abs/2609.29449

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