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An Improvement of the Upper Bound for the Number of Halving Lines of Planar Sets.
- Source :
- Symmetry (20738994); Jul2024, Vol. 16 Issue 7, p936, 14p
- Publication Year :
- 2024
-
Abstract
- In this paper, we provide improvements in the additive constant of the current best asymptotic upper bound for the maximum number of halving lines for planar sets of n points, where n is an even number. We also improve this current best upper bound for small values of n, namely, 106 ≤ n ≤ 336 . To obtain this enhancements, we provide lower bounds for the sum of the squares of the degrees of the vertices of a graph related to the halving lines. [ABSTRACT FROM AUTHOR]
- Subjects :
- DISCRETE geometry
POINT set theory
ADDITIVES
Subjects
Details
- Language :
- English
- ISSN :
- 20738994
- Volume :
- 16
- Issue :
- 7
- Database :
- Complementary Index
- Journal :
- Symmetry (20738994)
- Publication Type :
- Academic Journal
- Accession number :
- 178695653
- Full Text :
- https://doi.org/10.3390/sym16070936