An Improvement of the Upper Bound for the Number of Halving Lines of Planar Sets
Estrella Alonso, M. Dolores López González, Javier Rodrigo Hitos · Symmetry · 2024
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.