On Dirac and Motzkin Problem in Discrete Geometry.
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| Title: | On Dirac and Motzkin Problem in Discrete Geometry. |
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| 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] |
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| Database: | Engineering Source |
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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 ⌈ 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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| ISSN: | 09110119 |
| DOI: | 10.1007/s00373-025-02913-w |
