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arXiv · 2501.18406

On Dirac and Motzkin problem in discrete geometry

Jan Florek
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Abstract

Dirac and Motzkin conjectured that any set X of $n$ non-collinear points in the plane has an element incident with at least $\lceil \frac{n}{2} \rceil$ lines spanned by X. In this paper we prove that any set X of $n$ non-collinear points in the plane, distributed on three lines passing through a common point, has an element incident with at least $\lceil \frac{n}{2} \rceil$ lines spanned by X.

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Jan Florek. 2025-01-30. On Dirac and Motzkin problem in discrete geometry. https://arxiv.org/abs/2501.18406

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