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On Dirac and Motzkin Problem in Discrete Geometry.

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Title: On Dirac and Motzkin Problem in Discrete Geometry.
Authors: Florek, Jan1 (AUTHOR) jan.florek@pwr.edu.pl
Source: Graphs & Combinatorics. Jun2025, Vol. 41 Issue 3, p1-5. 5p.
Subjects: Discrete geometry, Logical prediction
Abstract: Dirac and Motzkin conjectured that any set X of n non-collinear points in the plane has an element incident with at least ⌈ n 2 ⌉ 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 ⌈ n 2 ⌉ lines spanned by X . [ABSTRACT FROM AUTHOR]
Copyright of Graphs & Combinatorics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Dirac and Motzkin conjectured that any set X of n non-collinear points in the plane has an element incident with at least ⌈ n 2 ⌉ 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 ⌈ n 2 ⌉ lines spanned by X . [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Graphs & Combinatorics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1007/s00373-025-02913-w
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        Text: English
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      – SubjectFull: Logical prediction
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              Text: Jun2025
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